### What are allowed quantized energies of the half-oscillator

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##### Reference no: EM13957159

Consider the corresponding problem for a particle confined to the right-hand half of a harmonic-oscillator potential:

V(x) = infinity, x< 0
V(x) = (1/2)Cx^2, x >= 0

a. Compute the allowed wave function for stationary states of this system with those for a normal harmonic oscillator having the same values of m and C.

b. What are the allowed quantized energies of the half-oscillator?

c. Devise a classical mechanical system that would be a macroscopic analog of this quantum-mechanical system.

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