The raising and lowering operators for the quantum harmonic oscillator satisfy
for energy eigenstates
with energy
.
Which of the following gives the first-order shift in the
energy level due to the perturbation

where
is constant?
A.
B.
C.
D.
E.
The energy
with
and 
Raising and lowering operators:

Answer: E
for energy eigenstates
where
A.
B.
C.
D.
E.
(GR0177 #94)
Solution:
The energy
with
Raising and lowering operators:
Answer: E
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