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Quantum Mechanics, one-dimensional box problem

  • Thread starter 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 ?
 

robphy

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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

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

Daniel.
 

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