Quantum Mechanics, one-dimensional box problem

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Homework Help Overview

The discussion revolves around the one-dimensional quantum mechanics box problem, specifically focusing on the energy eigenfunctions and eigenvalues associated with a box defined between -a/2 and a/2. Participants are exploring the mathematical formulation of the wavefunctions and the conditions that must be satisfied at the boundaries.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the general form of the wavefunction and the boundary conditions required for continuity. Questions arise regarding the determination of the wave number "k" and the implications of the box's boundaries on the eigenfunctions. There is also a query about the notation used for the wavefunction.

Discussion Status

The discussion is active, with participants offering insights into the properties of the wavefunctions and questioning the original poster's understanding of the problem setup. Some guidance has been provided regarding the periodicity conditions that relate to the allowed values of "k" and the resulting energy spectrum.

Contextual Notes

There is a mention of potential confusion regarding the notation of the wavefunction, as well as the implications of the box's boundaries on the eigenfunctions. The original poster's understanding of the problem setup appears to be incomplete, as they seek clarification on specific aspects of the solution.

danai_pa
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What are the energy eigenfunctions and eigenvalues for the one-dimensional box problem describ above if the end of the box are at -a/2 and a/2

I can find the solution of this problem Phi(x) = Asin kx + Bcos kx
and property of wavefunction is continuous at boundary
Phi(x=-a/2) = Phi(x=a/2)=0
but i don't understand to find k (wave number), please help me
 
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danai_pa said:
What are the energy eigenfunctions and eigenvalues for the one-dimensional box problem describ above if the end of the box are at -a/2 and a/2

I can find the solution of this problem Phi(x) = Asin kx + Bcos kx
and property of wavefunction is continuous at boundary
Phi(x=-a/2) = Phi(x=a/2)=0

What is the problem "described above"?

And do you perhaps mean Psi instead of Phi ?
 
Can you sketch your eigenfunctions?
(I'm assuming you've done the box problem with ends x=0 to x=a. Hopefully you realize that the choice of origin shouldn't change the shape of the eigenfunctions.)
See any pattern? any grouping of the eigenfunctions?
 
The periodicity conditions shouls give you the allowed "k" values from which you can get the energy spectrum.

Daniel.
 

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