# Conventional description of the matter wave

• I
• George444fg
In summary, the problem at hand involves finding the state function solution for a quantum wave function that does not change when shifted in position or time. The suggested solution is sin(kx-wt)+acos(kx-wt), with the coefficient a=±i. To maintain a positive energy state, it is determined that the coefficient of the cosine term must be +i.
George444fg
TL;DR Summary
Conventional description of the matter wave
I have been working on a relatively simple problem. Just take a quantum wave function for which a physical requirement is that an arbitrary displacement of x or an arbitrary shift of t should not alter the character of the wave, and I want to find the state function solution. A possible guess that works is sin(kx-wt)+acos(kx-wt). I found out that a=±i, and then I have to say which one corresponds to the convention. I said that it must be that γγ=i, because if it was -i, then the time derivative of the state function would have been negative, and using Schrodinger equation that would imply negative energy states. Am I right?

Yes, you are correct. The convention that is usually used is that the wave function should have a positive energy, and so the time derivative of the wave function should be positive. Therefore, the coefficient of the cosine term must be +i in order for the wave function to satisfy this requirement.

Replies
9
Views
1K
Replies
2
Views
1K
Replies
17
Views
2K
Replies
2
Views
1K
Replies
9
Views
2K
Replies
4
Views
1K
Replies
6
Views
1K
Replies
36
Views
4K
Replies
4
Views
2K
Replies
31
Views
4K