Question

particle of mass m is moving in a one-dimensional potential V
(x) such that ⎧

⎨ mω2 x2 ifx>0 V (x) = 2

⎩ +∞ if x ≤ 0

(a) Consider the motion classically. What is the period of
motion in such potential and the corresponding cyclic
frequency?

(b) Consider the motion in quantum mechanics and show that the
wave functions of the levels in this potential should coincide with
some of the levels of a simple oscillator with the potential mω2
x2/2 at all (positive and negative) x.

(c) Find the spectrum of the levels in the potential V (x).
How is the spacing between consequtive energy levels related to the
frequency of the classical motion?

Answer #1

1. Consider a particle with mass m in a one dimensional
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V (x)= 0, x<0
V(x)=V0, x>0
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