The ground state of the infinite square wel

In summary, the ground state of the infinite square well is not an eigenfunction of momentum. This can be seen by writing down the ground state in x representation and applying the momentum operator, which does not result in a multiple of the ground state. This is also supported by the example of a classical ball bouncing between two walls, where the momentum is not conserved even though kinetic energy is. However, the caveat is that this is not always applicable in quantum mechanics.
  • #1
ttiger654
2
0
Is the ground state of the infinite square well an eigenfunction of momentum?? If so, why. If not, why not??
 
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  • #2
You should take these kinds of questions to the homework section of the forum.
 
  • #3
Write down the ground state in x representation and try the momentum operator on it. Do you get back a multiple of the ground state?
 
  • #4
I think that Dick has adequately covered the mathematical aspect of it. Now let's think about some common sense physics. Imagine a classical ball bouncing elastically between two rigid walls (let's neglect gravity here). So kinetic energy is conserved at each collision, right? But the momentum is obviously not conserved, as the ball spends half its time going left and the other half going right. (Recall that momentum has direction).

Caveat: Normally, thinking of quantum particles as classical particles is ill advised, but this is one of those situations in which the classical result carries over to the quantum scale.
 

What is the infinite square well?

The infinite square well is a theoretical model used in quantum mechanics to represent a particle confined to a one-dimensional space with infinite potential walls on either side.

What is the ground state of the infinite square well?

The ground state of the infinite square well refers to the lowest energy state that a particle can have within the potential well. In this state, the particle has a probability of being found at any position within the well, but is most likely to be found at the center.

How is the ground state of the infinite square well calculated?

The ground state energy of the infinite square well can be calculated using the Schrödinger equation, which takes into account the potential energy of the well, the mass of the particle, and the boundary conditions of the well.

What is the significance of the ground state in the infinite square well?

The ground state is significant because it represents the lowest energy state that a particle can have within the well. It is also the starting point for calculating higher energy states and understanding the behavior of particles within the well.

Can there be multiple ground states in the infinite square well?

No, there can only be one ground state in the infinite square well. This is because the potential well has infinite potential walls, meaning that the particle cannot have a lower energy state than the ground state.

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