Four Parts - Mostly confused by the notation. Could likely do it otherwise. Best

Question

Four Parts - Mostly confused by the notation. Could likely do it otherwise.

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A particle of mass m in a harmonic oscillator with frequency omega, at time t = 0 is in a linear superposition of the ground and the first excited eigenstates, specifically, it has wave function Normalize the wave function. Find the coefficients cn in the series expansion If the energy is measured at time t, what are the possible values and what are the probabilities? Find the expectation value of the Hamiltonian in this state. Find the expectation value of the momentum of the particle at time t, . Find the value of the phase such that rang reaches its maximum value at time t = 0.

Explanation / Answer

infohost.nmt.edu/~jrembold/pdfs/Resources/Quantum1.pdf Http://Galileo.phys.Virginia.EDU/classes/751.mf1i.fall02/SimpleHarmonicOscillator.htm

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