# Group velocity in infinite square well

• 8Apeiron8
In summary, the conversation is about calculating the group velocity of a wave package in an infinite square well. However, the well only allows for standing wave solutions, making it impossible to define a group velocity. The conversation also references equations and links for further information on the subject.
8Apeiron8
ello everybody,

how can I calculate the group velocity of a wave package in an infinite square well?

I know only how it can be calculated with a free particle, the derivation of the dispersion relation at the expectation value of the moment.

But in the well, there are only discrete values of k allowed.

It would help a lot if someone could send me a link or give a little help,

thanks

Apeiron

An infinite well only allows for standing waves solutions for which it does not make sense to define group velocity.

Dr Du...
Standing waves!...yes, I wondered about that before I posted and figured it was
'too simple'...actually I also figured standing waves COULD support a group velocity
but having never studied that, dismissed the idea...

Last edited:

## 1. What is group velocity in an infinite square well?

The group velocity in an infinite square well refers to the average velocity at which a wave packet (a group of waves) travels through the well. It is a property of quantum mechanics and is related to the energy and momentum of the particles in the well.

## 2. How is group velocity calculated in an infinite square well?

The group velocity in an infinite square well can be calculated using the formula vg = (2E/m)^1/2, where vg is the group velocity, E is the energy of the particle, and m is its mass. This formula assumes that the particle is in its ground state.

## 3. Why is the group velocity in an infinite square well constant?

In an infinite square well, the particle is confined to a specific region and has a discrete set of allowed energies. This leads to a constant group velocity because the particle is not able to accelerate or decelerate within the well. Any changes in energy will result in a different wave function and a new constant group velocity.

## 4. How does the group velocity change with the size of the infinite square well?

The group velocity in an infinite square well is inversely proportional to the size of the well. This means that as the size of the well increases, the group velocity decreases. This relationship is a consequence of the formula for group velocity, which includes the width of the well in its calculation.

## 5. Can the group velocity in an infinite square well exceed the speed of light?

No, the group velocity in an infinite square well is always less than the speed of light. This is because the particles in the well are described by quantum mechanics and are subject to the laws of relativity, which state that nothing can travel faster than the speed of light.

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