Simple Harmonic Oscillator. Suppose that a particle ofmass
Chapter 38, Problem 38.52(choose chapter or problem)
Simple Harmonic Oscillator. Suppose that a particle ofmass ra is trapped not in a square well, but in one whosepotential energy is that of a simple harmonic oscillator:U(x) = \Cx2. That is, if the particle is displaced from x = 0,a restoring force F = Cx acts on it, where C is constant.(a) Sketch this potential energy. (b) Show that if/ = Ae~B*2is a solution to the Schrodinger equation and that the energyof this state is E = \ ho), where o) = \/C /m (as classically,Eq. 14-5) and B = raw/2/L [Note: This is the groundstate, and this energy \ha) is the zero-point energy for aharmonic oscillator. The energies of higher states areEn = (n + l)ha), where n is an integer.]
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