IV. Consider a simple harmonic oscillator in one dimension with the usual Hamnil- tonian Ho=+ a) The eigenfunction of the ground state can be written as o(r) = Ne Determine the constants N and a. b) What is the eigenvalue of the ground state? c) At timet = 0, the wavefunction is where (z) is the exact eigenstate of the harmonic oscillator with eigenvalue h(n+ 1/2). d) Give r,t) for t20. e) What is the parity of this state? Does it change with time? f) What is the average value of the energy for this state? Does it change with time?
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