### How do you know if a wavefunction is normalized?

Normalizing a wave function means multiplying it by a constant that ensures the sum of probabilities for finding the particle equals 1. In simpler terms, it ensures that the wave function accurately reflects the particle’s existence.

Think of it like a pie chart. Each slice of the pie represents the probability of finding the particle in a specific region. If all the slices add up to 100%, you have a complete picture of where the particle could be. The same applies to a normalized wave function. It gives you a complete picture of the particle’s probability distribution.

You can determine if a wave function is normalized by performing a mathematical operation called integration. This involves calculating the area under the curve of the wave function squared over all space. If the result of this integration is 1, the wave function is normalized.

A normalized wave function is a crucial concept in quantum mechanics, as it ensures that the probability of finding a particle in a specific location is accurately represented. It’s like having a reliable map that tells you exactly where you’re likely to find a treasure.

### Are wave functions always normalizable?

The answer is no, not all wavefunctions can be normalized.

Let’s break it down. A wavefunction represents the probability of finding a particle in a specific location at a given time. Normalization means that the probability of finding the particle somewhere in the entire space must equal 1. This makes sense, right? The particle has to be somewhere!

Normalization is essential for describing the physical reality of a particle. However, some wavefunctions don’t satisfy this condition. Imagine a particle that can travel infinitely far. The probability of finding it in any finite region would be infinitesimally small, leading to an unnormalizable wavefunction.

Think of it this way: if you’re trying to find a specific grain of sand on a beach, you’re more likely to succeed if you know the beach is limited. However, if the beach stretches infinitely, your chances of finding that grain of sand become practically zero. Similarly, for a wavefunction to be normalizable, it needs to be confined to a finite region.

In quantum mechanics, we often deal with wavefunctions that are assumed to be square-integrable and normalized. This means that the integral of the square of the wavefunction over all space is finite, allowing us to normalize it. But remember, not all wavefunctions are square-integrable, and therefore not all are normalizable.

So, while we often use normalized wavefunctions, it’s important to keep in mind that this is a simplification that doesn’t always hold true. Understanding the limitations of normalization helps us appreciate the full scope of quantum mechanics.

### How do you know if a wave function is acceptable?

So, you’re working with wave functions, which are mathematical descriptions of particles in quantum mechanics. You might be wondering: how do you know if a wave function is acceptable? There are a few key criteria to consider.

First, a wave function must be continuous. This means that there are no sudden jumps or breaks in the function’s value. Imagine a smooth, unbroken curve; that’s what you want your wave function to look like.

Second, the wave function must be smooth, which means that its first derivative (the rate at which its value changes) is also continuous. Think of it this way: not only should the function itself be smooth, but the slope of the function should also change smoothly.

Third, the wave function must approach zero as the position goes to positive or negative infinity. This makes sense if you think about a particle; it’s not likely to be found infinitely far away.

Finally, a wave function must be normalizable, meaning it’s possible to calculate a probability of finding a particle within a given region. This makes sure that the wave function represents a real physical system.

Delving Deeper into Acceptable Wave Functions

Let’s break down these criteria a bit further:

Continuity ensures that the wave function describes a physical system without any abrupt changes. Imagine a wave function describing an electron orbiting a nucleus; the electron’s position can’t suddenly jump from one point to another without going through the points in between.

Smoothness means that the wave function doesn’t have any sharp corners or kinks. This relates to the momentum of the particle, which is connected to the rate of change of the wave function. Imagine a particle moving smoothly along a path; its wave function should reflect this smoothness.

Going to zero at infinity ensures that the probability of finding the particle infinitely far away is zero, which makes physical sense. For example, you wouldn’t expect to find an electron infinitely far away from an atom.

Normalizability means that the wave function can be scaled to give a total probability of 1 for finding the particle somewhere in space. This ensures that the wave function is a realistic representation of the particle. You can think of it like a probability distribution – all the probabilities of finding the particle in different places should add up to 100%.

These criteria help us understand what makes a wave function physically valid. They ensure that the wave function accurately describes the behavior of a particle in a quantum mechanical system, ensuring that the predictions made by the theory match up with experimental observations.

### What is the condition for normalization of a wave function?

∫∞−∞|ψ(x,t)|²dx=1

This equation means that the integral of the square of the wave function over all space must equal 1. This condition ensures that the wave function is properly normalized and that the probability of finding the particle somewhere in space is equal to 1.

Let’s break this down further. ψ(x,t) represents the wave function, which describes the state of a particle at a given position x and time t. The absolute value squared, |ψ(x,t)|², represents the probability density of finding the particle at that position and time.

The integral ∫∞−∞|ψ(x,t)|²dx sums up the probability density over all possible positions of the particle. This integral must equal 1, indicating that there is a 100% chance of finding the particle somewhere within the defined space.

Think of it like this: imagine you have a bucket of marbles. The probability of finding a marble in the bucket is 1. You can’t find a marble outside of the bucket. Similarly, the probability of finding a particle in the entire universe is 1. It has to be somewhere.

The normalization condition is a fundamental principle in quantum mechanics. It ensures that the wave function is a physically realistic representation of the particle’s state. It’s a way of ensuring that the probabilities we calculate from the wave function make sense. Without normalization, the probabilities wouldn’t add up to 1, which would mean we were missing something.

In summary, the normalization condition ensures that the wave function accurately reflects the probability of finding a particle at a particular point in space and time. This is a crucial concept in understanding how quantum mechanics works.

### How to show that a function is normalised?

To normalize a wave function, you have to integrate its squared magnitude over all space. If the result of this integration is 1, then you’ve successfully normalized your wave function.

Let’s break this down a bit.

Why do we normalize wave functions?

In quantum mechanics, the wave function describes the probability of finding a particle in a particular location. The squared magnitude of the wave function represents the probability density. Since the probability of finding the particle *somewhere* must be 1, we need to make sure the integral of the probability density over all space equals 1. This is what it means to normalize the wave function.

How do we normalize a wave function?

1. Calculate the squared magnitude: This means squaring the wave function and then taking its absolute value.

2. Integrate over all space: This means integrating the squared magnitude of the wave function over all possible values of the position.

3. Divide by the result: Divide the original wave function by the result of the integration. This ensures that the integral of the squared magnitude of the new wave function is 1.

Here’s a simple example:

Let’s say our wave function is ψ(x) = Ae^{-x^2}, where A is a constant.

1. Calculate the squared magnitude: |ψ(x)|² = A²e^{-2x^2}

2. Integrate over all space: We need to integrate this from -∞ to +∞. The result of this integration is A²√(π/2).

3. Divide by the result: We divide the original wave function by this result to get ψ(x) = (1/√(π/2))e^{-x^2}.

This new wave function is now normalized. The integral of its squared magnitude over all space is 1, meaning that the probability of finding the particle somewhere in space is 1.

A few important things to remember:

* Not all wave functions are initially normalized. You may need to normalize them yourself to ensure they are physically meaningful.

* Normalization is an important step in many quantum mechanical calculations.

* The process of normalization ensures that the probability interpretation of the wave function is consistent.

### How do you test for normalization?

You can use graphical methods like histograms or Q-Q probability plots. These methods visually represent your data. A histogram shows the frequency of different values in your data set, while a Q-Q plot compares the quantiles of your data to the quantiles of a normal distribution.

Analytical methods like the Shapiro-Wilk test and the Kolmogorov-Smirnov test are also helpful. These tests provide a statistical measure of how well your data fits a normal distribution. The Shapiro-Wilk test is best for smaller sample sizes, while the Kolmogorov-Smirnov test is better for larger ones.

Think of it this way: Imagine you’re trying to fit a square peg into a round hole. Graphical methods are like looking at the peg and the hole and seeing if they look like they’ll fit. Analytical methods are like using a measuring tape to see if the dimensions match up perfectly.

Here’s a little more about how these methods work:

Graphical Methods

Histograms: If your data is normally distributed, a histogram will look like a bell-shaped curve. This is also called a normal distribution curve.

Q-Q probability plot: If your data is normally distributed, the points on a Q-Q plot will fall along a straight line. If the points deviate significantly from a straight line, it indicates that your data is not normally distributed.

Analytical Methods

Shapiro-Wilk test: This test calculates a statistic that measures how well your data fits a normal distribution. A p-value is generated, and if it’s less than 0.05, it means that there is strong evidence to suggest that your data is not normally distributed.

Kolmogorov-Smirnov test: Similar to the Shapiro-Wilk test, this test also provides a p-value. A p-value less than 0.05 indicates that your data is not normally distributed.

It’s important to keep in mind that no single test is perfect. It’s a good idea to use multiple methods to assess normalization. And remember, even if your data is not perfectly normally distributed, it might still be close enough to use statistical methods that assume normality.

### Why the wave function for a particle must be normalizable?

Let’s break this down a bit. Imagine you’re trying to find your keys. You know they’re somewhere in your house, but you don’t know exactly where. You might start by looking in the most likely places, like your pockets or by the door. If you keep searching, you’ll eventually find your keys, but you can’t be in two places at once, right?

The same concept applies to particles. We can’t know exactly where a particle is at any given time, but we can describe the probability of finding it in a certain region of space. This is where the wave function comes in. It’s a mathematical function that describes the probability of finding a particle at a specific point in space.

Normalizability is a property that ensures that the probability of finding the particle in all of space adds up to 1. Think of it like this: if you add up the probabilities of finding your keys in every room of your house, you’ll get 100% (or 1). Similarly, if you add up the probabilities of finding a particle in every point in space, you’ll get 100% (or 1).

If the wave function weren’t normalizable, it would mean that there was a possibility of finding the particle in more than one place at the same time. But that’s not how the universe works! Particles have to be somewhere, and the wave function has to reflect that.

### What must a non normalized wave function have?

Think of it this way: Imagine you have a bag of marbles. If the bag is normalized, the marbles inside represent the probability of finding a particle in a specific state. Now, if the bag is non-normalized, it means we’ve got an infinite number of marbles, and we can’t accurately determine the probability of finding the particle.

Let’s get more technical. A wave function, represented by the Greek letter ψ, describes the state of a quantum particle. In the context of quantum mechanics, the norm of the wave function is calculated by integrating the square of the wave function over all space. A normalized wave function has a norm of 1, which means the probability of finding the particle in any state is 100%.

Now, a non-normalized wave function is a bit different. Because of the infinite number of marbles in our bag analogy, it essentially means the probability of finding the particle anywhere is unbounded and doesn’t add up to 1.

While this might seem like a theoretical oddity, it’s important to understand the concept of normalization in quantum mechanics. The key takeaway is that non-normalized wave functions don’t provide us with a concrete probability of finding a particle in a given state. They lack the finite sum required to properly define probability.

It’s also worth noting that while non-normalized wave functions are interesting theoretical concepts, they are not used in practical calculations. To make use of wave functions in real-world situations, they must be normalized.

### Are plane waves normalizable?

Let’s dive deeper into why plane waves are not normalizable, and why this is important for understanding wave functions in quantum mechanics.

Imagine a particle that is perfectly localized in space. It’s not spread out at all – it’s just sitting in one place. This particle can be represented by a wave function that is zero everywhere except at that single point. This kind of wave function is called a delta function, and it’s a perfect example of a normalizable function. The integral of its squared amplitude over all space is finite, and the probability of finding the particle in all of space is 1.

Now, think about a plane wave. It’s the opposite of a localized particle. It’s spread out over all space, and its amplitude is constant. This means that the integral of its squared amplitude over all space is infinite, and the probability of finding the particle in all of space is greater than 1. This makes no physical sense.

You might be wondering why we even bother with plane waves if they’re not normalizable. The answer is that they are a very useful mathematical tool. We can use them to represent waves of a specific frequency and momentum, even though they don’t represent real physical particles. This means that we can use them to build up more complex wave functions that do represent real physical particles. In other words, plane waves are like the building blocks of the wave functions that we use to describe the behavior of particles in quantum mechanics.

Think of it like this. A plane wave is like a pure tone – it has a single frequency. But real sounds are made up of many different frequencies. We can use a combination of pure tones to build up a complex sound. Similarly, we can use a combination of plane waves to build up a wave function that represents a real physical particle.

So, while plane waves aren’t normalizable, they are still a very important part of quantum mechanics. They allow us to use a mathematical framework to understand the behavior of particles, even though they don’t represent real physical particles themselves.

See more here: Are Wave Functions Always Normalizable? | How To Tell If A Wave Function Is Normalizable

### Should wavefunctions be normalizable or square-integrable?

The key is that they should be normalizable. This simply means that the integral of the squared magnitude of the wavefunction over all space must be finite. Why is this important? Because the integral represents the probability of finding the particle somewhere in space, and that probability should always be less than or equal to 1.

Now, you might be wondering about square-integrability. A function is square-integrable if the integral of its squared magnitude over all space is finite. It turns out that all normalizable functions are also square-integrable, but not all square-integrable functions are normalizable. This is where the “almost everywhere” concept comes in.

Think of it this way: a normalizable function needs to “settle down” at infinity, meaning its value must approach zero as you move further and further away from the origin. This ensures that the total probability of finding the particle somewhere is finite. However, a square-integrable function might have some “bumps” or “spikes” at infinity, as long as they don’t cause the integral to diverge.

This is why we say that the allowed wavefunctions are the non-vanishing square-integrable functions. These functions are always normalizable, meaning the probability of finding the particle somewhere in space is always finite. In essence, the wavefunctions should be “well-behaved” at infinity, ensuring that the probability of finding the particle is physically meaningful.

The concept of “almost everywhere” is a bit more nuanced. It means that the functions are equal everywhere except possibly on a set of points with zero measure. This is important because it allows us to consider functions that might have some “spikes” or “jumps” at specific points, as long as those points don’t affect the overall integrability of the function. This makes the theory more robust and allows for a wider range of possible wavefunctions.

### Why must wavefunctions be normalized?

Think of it this way: imagine you’re playing a game where you have to find a hidden treasure. The wavefunction is like a map that tells you the likelihood of finding the treasure in different locations. The map itself doesn’t guarantee you’ll find the treasure, but it gives you a sense of where to look.

Now, for this map to be useful, the total probability of finding the treasure somewhere on the map must be 1. This means that there’s a 100% chance of finding the treasure somewhere within the boundaries of the map. If the total probability was greater than 1, it would mean there’s a higher than 100% chance of finding the treasure, which doesn’t make sense. On the other hand, if the total probability was less than 1, it would mean there’s a chance the treasure might be somewhere outside the map, which again doesn’t make sense.

That’s where normalization comes in. It’s a mathematical process that ensures the total probability represented by the wavefunction is always 1. This way, the wavefunction remains a reliable tool for understanding the probabilities associated with quantum particles.

To be more precise, the normalization condition states that the integral of the squared magnitude of the wavefunction over all space must equal 1. This integral represents the total probability of finding the particle in any possible location. By ensuring this integral equals 1, we guarantee that the probability of finding the particle somewhere is complete and accurate.

In simpler terms, normalizing the wavefunction makes sure the map of probabilities is complete and consistent, ensuring we don’t miss any potential hiding spots for our treasure!

### How do you find a normalized wavefunction?

To find the expectation value of position, we’ll use the following equation:

⟨x⟩ = ∫ψ*(x) x ψ(x) dx

This equation tells us to multiply the wavefunction by the position operator (which is simply x in this case), then multiply the result by the complex conjugate of the wavefunction, and finally integrate over all space.

Since our wavefunction is real, its complex conjugate is the same as the original function. This makes our calculation a bit simpler.

Let’s break down the steps:

1. Substitute the wavefunction:

We’ll plug in ψ(x) = e−|x|/x0/ x0−−√ into the equation for the expectation value.

2. Evaluate the integral:

We’ll need to integrate the resulting expression over all space. This involves separating the integral into two parts: one for x > 0 and one for x < 0, due to the absolute value in the exponent.
3. Simplify and solve:
We'll then simplify the integrals and evaluate them to get the final answer, which represents the expectation value of position.
Here's why this calculation is important:
The expectation value of position tells us the average position of the particle, given its wavefunction. This is a fundamental concept in quantum mechanics because it allows us to predict the outcome of measurements on a quantum system. For example, if we were to measure the position of the particle described by this wavefunction many times, the average of those measurements would be equal to the expectation value of position.
Let's talk about normalization:
We need to make sure our wavefunction is normalized. Normalization means that the probability of finding the particle somewhere in space is equal to 1. This is done by ensuring that the integral of the square of the wavefunction over all space equals 1.
In our case, the wavefunction is already normalized. We can see this because the term 1/x0−−√ is included in the wavefunction. This term ensures that the integral of the square of the wavefunction over all space equals 1.
Let's wrap up:
Understanding how to calculate the expectation value of position for a normalized wavefunction is crucial in quantum mechanics. It allows us to connect the abstract world of wavefunctions to the tangible world of measurements.

### Can a plane wavefunction be normalized?

You might have heard that a plane wave function can’t be normalized. This is because plane waves extend infinitely in space, meaning their wavefunction doesn’t decay to zero at infinity. This makes it impossible to calculate the integral of the squared wavefunction over all space, which is what we need to do to normalize it.

Think of it this way. Normalization is like finding the total probability of finding a particle in all of space. For a plane wave, the probability of finding the particle is spread out evenly over the entire universe, making the total probability infinite.

However, this doesn’t mean plane waves are useless! They’re still important for describing the behavior of particles, especially when we’re interested in their momentum.

In fact, plane waves represent particles with a specific momentum. It’s like saying the particle is moving in a specific direction with a certain speed. While they can’t be normalized in the traditional sense, we can still use them to describe real-world scenarios. We just need to be aware of their limitations.

Here’s a way to think about it: in reality, we never encounter a truly infinite plane wave. Instead, we might have a wavepacket, which is a localized wave that is made up of a superposition of plane waves. These wavepackets can be normalized because they are confined to a specific region of space.

So, while a plane wave itself can’t be normalized, the idea of plane waves is still crucial in understanding the behavior of particles. And, by combining multiple plane waves, we can create wavepackets that *can* be normalized.

Let me know if you have any more questions about plane waves and normalization!

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### How To Tell If A Wave Function Is Normalizable

Okay, so you’re diving into the world of quantum mechanics and you’ve encountered this thing called a wave function. It’s supposed to describe the state of a particle, but how do you know if it’s actually a valid description? That’s where the concept of normalizability comes in.

Think of it this way: Imagine you’re trying to describe the weather. You might say “It’s sunny and warm,” or “It’s rainy and cold.” Those are valid descriptions, right? But what if you said, “It’s infinitely sunny and infinitely warm”? That doesn’t make sense. It’s not a physically realistic description.

The same goes for wave functions. They need to be normalizable to be physically realistic. In other words, the probability of finding the particle somewhere in space should be a finite value, not infinity.

What Does Normalizable Mean?

Let’s break down normalizability into simpler terms. A wave function is considered normalizable if you can find a constant that you can multiply it by to make sure the probability of finding the particle *anywhere* in space adds up to 1.

Think about it like this: Let’s say you have a bag of marbles, and you want to know the probability of picking a red marble. You could count the total number of marbles and the number of red marbles. Then, you could divide the number of red marbles by the total number of marbles. That would give you the probability of picking a red marble.

The same principle applies to wave functions. We can’t directly “count” particles, but we can use the wave function to calculate the probability of finding the particle in a certain region of space. To make sure our probabilities add up to 1 (because the particle *has* to be somewhere), we need to normalize the wave function.

How to Determine if a Wave Function is Normalizable

So, how can you tell if a wave function is normalizable? There are a couple of ways to approach this:

1. The Integral Test:

The most common way to check if a wave function is normalizable is by integrating its square over all space. This is like adding up all the probabilities of finding the particle in each tiny region of space.

Let’s say you have a wave function represented by the symbol ψ (psi). Here’s how you do the integral test:

– Square the wave function: |ψ(x)|². This gives you the probability density, which tells you the probability of finding the particle at a specific point in space.

– Integrate this probability density over all space. In other words, add up the probability density for all possible positions of the particle.

– If the result of this integration is a finite value, then the wave function is normalizable. If it’s infinite, the wave function is not normalizable.

2. Look for Singularities:

Another way to think about normalizability is to look for singularities in the wave function. A singularity is a point where the wave function becomes infinite. If a wave function has a singularity, it’s likely not normalizable. This is because the probability of finding the particle at that singular point would be infinite, which is not physically possible.

Examples of Normalizable and Non-Normalizable Wave Functions

Let’s look at some examples to understand this better:

Example 1: A Normalizable Wave Function

– Wave function: ψ(x) = A*e^(-x²/2)

This is a common wave function used to describe the ground state of a harmonic oscillator. It’s normalizable because it’s well-behaved and goes to zero as x goes to infinity. The integral of its square over all space is finite.

Example 2: A Non-Normalizable Wave Function

– Wave function: ψ(x) = A

This wave function is a constant value for all x. It’s not normalizable because the integral of its square over all space is infinite. Imagine trying to find a particle in an infinitely long box with a constant probability density. The probability of finding it *anywhere* would be infinite.

Why Does Normalizability Matter?

So, why is normalizability such a big deal? Well, it’s crucial for a couple of reasons:

– Physical Realism: A normalizable wave function means that the probability of finding the particle somewhere in space is finite. This makes sense physically; a particle can’t exist in an infinite number of places at the same time!

– Meaningful Probabilities: A normalizable wave function allows us to calculate meaningful probabilities for finding the particle in specific regions of space. This is essential for making predictions about how particles behave.

FAQs

Q: What happens if a wave function is not normalizable?

A: If a wave function is not normalizable, it means it’s not a valid description of a physical particle. It’s like trying to describe a weather pattern with infinitely hot sunshine. It’s not physically realistic.

Q: Can I normalize a wave function that is not already normalizable?

A: It depends. In some cases, you might be able to modify a non-normalizable wave function to make it normalizable. This usually involves adding constraints or boundary conditions to the system. But in many cases, a non-normalizable wave function simply indicates that the system being described is not physically realistic.

Q: What are some examples of non-normalizable wave functions in physics?

A: Some examples of non-normalizable wave functions include:

– Free particle wave functions: In certain cases, free particle wave functions, which describe particles that are not subject to any potential, can be non-normalizable. This is because they can extend to infinity without decaying.

– Wave functions with singularities: Wave functions that have singularities, such as a point where the wave function goes to infinity, are typically non-normalizable.

Q: Is the concept of normalizability only relevant for particle wave functions?

A: No, the concept of normalizability is also important for other types of wave functions in quantum mechanics, like those describing electromagnetic fields or phonons (sound waves in solids).

Q: What are the implications for the interpretation of quantum mechanics if a wave function is not normalizable?

A: If a wave function is not normalizable, it throws a wrench into the standard interpretation of quantum mechanics, where probabilities are calculated based on the square of the wave function. In such cases, we need to rethink how we interpret the wave function and its relationship to the physical reality of the system.

Understanding normalizability is crucial for working with wave functions in quantum mechanics. It helps ensure that your calculations are physically realistic and allows you to make meaningful predictions about the behavior of particles.

### 3.2: Normalization of the Wavefunction – Physics LibreTexts

For instance, a plane-wave wavefunction \[\psi(x,t) = \psi_0\,{\rm e}^{\,{\rm i}\,(k\,x-\omega\,t)}\] is not square-integrable, and, thus, cannot be normalized. For such wavefunctions, the best we can say is that \[P_{x\,\in\, a:b}(t) \propto Physics LibreTexts

### Normalizable wave functions? – Physics Stack Exchange

You test a wave function for normalizability by integrating its square magnitude. If you get a finite result then it is normalizable. To spare you complicated Physics Stack Exchange

### Wave functions as being square-integrable vs. normalizable

This leads me to think that a wave function Ψ(x, t) Ψ ( x, t) must be normalizable, a stricter requirement than just square-integrable. In particular, f(x, t) = 0 f Physics Stack Exchange

### 3.6: Wavefunctions Must Be Normalized – Chemistry LibreTexts

Normalize the wavefunction of a Gaussian wave packet, centered on \(x=x_o\) with characteristic width \(\sigma\): \[\psi(x) = \psi_0 {\rm e}^{-(x-x_0)^{ 2}/(4 Chemistry LibreTexts

### Normalization of the Wavefunction – University of Texas at Austin

Normalization of the Wavefunction. Now, a probability is a real number between 0 and 1. An outcome of a measurement which has a probability 0 is an impossible outcome, Home Page for Richard Fitzpatrick

### Wave function – Wikipedia

In summary, the set of all possible normalizable wave functions for a system with a particular choice of basis, together with the null vector, constitute a Hilbert space. Not Wikipedia

### 6.1: Non-normalizable Wavefunctions – Physics LibreTexts

Let us investigate the two functions. Remembering that \[\hat{p}=\dfrac{ℏ}{i} \dfrac{∂}{∂ x}\] we find that \(ϕ ( x )\) (Equation \ref{6.1}) represents the sum of two states, Physics LibreTexts

### 7.2: Wave functions – Physics LibreTexts

In quantum mechanics, the state of a physical system is represented by a wave function. In Born’s interpretation, the square of the particle’s wave function represents the Physics LibreTexts

### normalizable – USNA

The wavefunction must be normalizable, − ψ(x) 2 dx ∞ ∞ ∫=1. This has two implications: 1. The wavefunction ψ(x) must be finite everywhere. Normally a wave cannot have infinite United States Naval Academy

### Time evolution of normalized wave function – GitHub Pages

1 Wave function normalization. The wave function (x; t) that describes the quantum mechanics of a particle of mass m moving in a potential V (x; t) satis es the Schrodinger rashid-phy.github.io

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Link to this article: **how to tell if a wave function is normalizable**.

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