Calculating % Contribution of nth Wavefunction in Potential Well

In summary, the question asks for the percentage contribution of the (2x2-1)th infinite potential well wavefunction to the initial wavefunction of psi(x,t=0)=1/sqrt(L). The even values of n are excluded, possibly due to their relation to Fourier series. It may be helpful to use the coefficient equation and determine the energy level.
  • #1
Caldo120
3
0

Homework Statement



What fraction (as a percentage) does the n=(2x2-1)th infinite potential well wavefunction contribute to the 'classical' initial wavefunction psi(x,t=0)=1/sqrt(L) ? (Why are the even n excluded?)

Homework Equations



psi(x,t=0) = 1 / sqrt(L)

The Attempt at a Solution



generally pretty dumbfounded with this, our lecturer hasn't went through a worked example and i can't find any related equations in my notes. Any help on the question would be greatly appreciated. I intend to ask my lecturer about it as well and the lack of related material. I think it may have something to do with Fourier series?

Thanks,

Calum
 
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  • #2


use the coefficient equation if you know what that is. And what energy level is that exactly
 

1. What is the formula for calculating the % contribution of nth wavefunction in a potential well?

The formula for calculating the % contribution of nth wavefunction in a potential well is P_n = |ψ_n|^2/∑|ψ_n|^2 * 100%, where P_n represents the % contribution, ψ_n represents the nth wavefunction, and the summation is taken over all possible wavefunctions.

2. How is the % contribution of nth wavefunction affected by changes in the potential well?

The % contribution of nth wavefunction is affected by changes in the potential well as it depends on the shape and depth of the potential well. A deeper potential well will increase the % contribution of the lower energy wavefunctions, while a shallower potential well will increase the % contribution of the higher energy wavefunctions.

3. Can the % contribution of nth wavefunction be greater than 100%?

No, the % contribution of nth wavefunction cannot be greater than 100%. This is because the summation of all possible wavefunctions represents the total probability of finding the particle in the potential well, and this value cannot exceed 100%.

4. How does the % contribution of nth wavefunction relate to the probability of finding the particle in a specific energy state?

The % contribution of nth wavefunction is directly related to the probability of finding the particle in a specific energy state. The higher the % contribution of a particular wavefunction, the higher the probability of finding the particle in that energy state.

5. How can the % contribution of nth wavefunction be experimentally determined?

The % contribution of nth wavefunction can be experimentally determined by measuring the energy states of the particle in the potential well and using the formula P_n = |ψ_n|^2/∑|ψ_n|^2 * 100%. This will give the relative contribution of each wavefunction to the total probability of finding the particle in the potential well.

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