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Kinetic and potential energy of harmonic oscillator, virial

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1. Consider a particle moving in a harmonic oscillator potential V(x) = ½ kx2. A solution of the time-dependent Schrodinger equation is

cn n(x)*e -i * E(n) * t / h-bar

where the n are harmonic oscillator energy eigenstates.

a. Calculate the energy expectation value <H> and the kinetic energy expectation value
K(t) = < | | >

At any given time t, in terms of the constants cn. Show that your answers are real, even if the cn are complex.

b. Let be the time average of K(t). Show that = ½ <H>.

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The expert examines kinetic and potential energy of harmonic oscillator. Time-dependent Schrodinger equations are examined.

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