Quantum Mechanics, one-dimensional box problem

danai_pa

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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tyco05

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 ?

robphy

Homework Helper
Gold Member
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?

dextercioby

Homework Helper
The periodicity conditions shouls give you the allowed "k" values from which you can get the energy spectrum.

Daniel.

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