Finding the momentum uncertainty for a particle-in-a-box

In summary, the conversation discusses calculating the uncertainty in the momentum measurement of an electron-in-a-box system for its nth excited state. The normalized wave function and the use of the p operator are mentioned as key components in solving this problem. The individual seeking help is unsure of how to proceed but is open to real-time assistance.
  • #1
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Homework Statement


I'm looking at an electron-in-a-box with walls at x=0 and x=L; I want to calculate the uncertainty (delta p) in the measurement of its momentum: sqrt(<p^2>−<p>^2) for its nth excited state.

Homework Equations


The normalized wave function: psi_n(x)=sqrt(2/L)*sin(n*pi*x/L)

The Attempt at a Solution


I'm not even sure what the p operator is for this situation. Should I just take p as -ihbar(d/dx) and sandwich p^2 and p like so? sqrt(<psi_n* | p^2 | psi_n> - <psi_n* | p | psi_n>^2)

Thanks in advance. I'll be online for a while; feel free to pop in here (http://cosketch.com/Rooms/euftgwf) if you can spare a few minutes to show me in real time.
 
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  • #2
You have the right idea. Just crank it out now.
 

1. What is the meaning of "momentum uncertainty" for a particle-in-a-box?

The momentum uncertainty for a particle-in-a-box refers to the range of possible values for the momentum of a particle confined to a box of a certain size. It is a measure of the uncertainty or variability in the particle's momentum within the given space.

2. How is the momentum uncertainty calculated for a particle-in-a-box?

The momentum uncertainty is calculated using the Heisenberg uncertainty principle, which states that the product of the uncertainty in position and the uncertainty in momentum must be greater than or equal to a certain value. In the case of a particle-in-a-box, this value is determined by the size of the box and the energy of the particle.

3. Can the momentum uncertainty for a particle-in-a-box ever be zero?

No, according to the Heisenberg uncertainty principle, the product of the uncertainty in position and momentum cannot be zero. This means that there will always be some level of uncertainty in the momentum of a particle in a box, even if the box is very small or the particle's energy is very well-defined.

4. How does the size of the box affect the momentum uncertainty for a particle-in-a-box?

The size of the box directly affects the momentum uncertainty for a particle-in-a-box. A smaller box will result in a larger momentum uncertainty, while a larger box will result in a smaller momentum uncertainty. This is because the smaller the box, the more confined the particle's position is, leading to a larger uncertainty in its momentum.

5. Are there any other factors that can affect the momentum uncertainty for a particle-in-a-box?

Yes, in addition to the size of the box, the energy of the particle can also affect the momentum uncertainty. A higher energy particle will have a smaller momentum uncertainty, as it is more likely to be found at the edges of the box where its momentum is higher. Additionally, the shape and potential of the box can also impact the momentum uncertainty.

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