A particle of mass M is in an infinitely deep square well potential 
where
for 
, and
for 
.
A very small perturbing potential' is superimposed on such that
for
, and
for 
.
If
are the energy eigenfunctions for a particle in the infinitely deep square well potential, with 
being the ground state, which of the following statements is correct about the eigenfunction 
of a particle in the perturbed potential 
?
A.
B.
with 
for all odd values of n.
C. with for all even values of n.
D. with for all values of n.
E. None of the above
The eigenfunctions of the unperturbed infinite deep well form a complete set (or complete basis).
This means that any function can be represented by the old unperturbed infinite deep well.
Thus, the solution to the perturbed eigenfunction should look like .
Also, since the perturbed potential is also symmetrical with respect to the origin (as the original unperturbed potential was, too), one knows that all the odd terms should go to 0.
Answer: B
where
for , and
for .A very small perturbing potential
' is superimposed on such that
for
, and for .If
are the energy eigenfunctions for a particle in the infinitely deep square well potential, with being the ground state, which of the following statements is correct about the eigenfunction of a particle in the perturbed potential ?A.
B.
with for all odd values of n.C.
with for all even values of n.D.
with for all values of n.E. None of the above
(GR8677 #96)
Solution:The eigenfunctions of the unperturbed infinite deep well form a complete set (or complete basis).
This means that any function can be represented by the old unperturbed infinite deep well.
Thus, the solution to the perturbed eigenfunction should look like .
Also, since the perturbed potential is also symmetrical with respect to the origin (as the original unperturbed potential was, too), one knows that all the odd terms should go to 0.
Answer: B
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