A one-dimensional simple lharmonic oscillator is subjected to a small perturbing potential &V(2), producing a “dinple" at the center of the mo- tion. Thus p2 p2 H = +mw?x? + +V + 6V. 2m 2m 12 + a? Calculate the correction to the ground state energy of the oscillator to first orcder in A in the event that (a) a « Vh/muw, (b} a » Vh/mw. Hints: the norinalized ground state wave function of a simple harmonic: oscillator is u (r) exp(-muт* /2h), and dx %3D x2 + a?
A one-dimensional simple lharmonic oscillator is subjected to a small perturbing potential &V(2), producing a “dinple" at the center of the mo- tion. Thus p2 p2 H = +mw?x? + +V + 6V. 2m 2m 12 + a? Calculate the correction to the ground state energy of the oscillator to first orcder in A in the event that (a) a « Vh/muw, (b} a » Vh/mw. Hints: the norinalized ground state wave function of a simple harmonic: oscillator is u (r) exp(-muт* /2h), and dx %3D x2 + a?
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Transcribed Image Text:A one-dimensional simple lharmonic oscillator is subjected to a small
perturbing potential &V(x), producing a “dinple" at the center of the mo-
tion. Thus
p2
p2
H =
+mw?x? +
+V + 6V.
2m
2m
x² + a?
Calculate the correction to the ground state energy of the oscillator to first
orcder in A in the event that
(a) a « Vh/muw,
(b} a » Vh/mw.
Hints: the norinalized ground state wave function of a simple harmonic:
oscillator is
u (x.)
exp(-mwx? /2h),
and
dx
x2 + a?
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