A particle in the harmonic oscillator potential starts out at t = 0 in the state Ψ(x, 0) = A (5ψ0(x) + 12ψ1(x))
(a) [2 points] Find A.
(b) [5 points] Find <x> and <p> as a function of time.
(c) [3 points] Check Ehrenfest’s theorem that d<p>/dt = − <dV/dx>
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A particle in the harmonic oscillator potential starts out at t = 0 in the state...
A particle in the harmonic oscillator potential, V(x) - m2t2, is at time t 0 in the state ψ(x, t-0) = A3ψο(x) +4ψι (2)] where vn (z) is the nth normalized eigenfunction (a) Find A so that b is normalized. (b) Find ψ(x,t) and |ψ(x, t)12 (c) Find x (t) and p)(t). what would they be if we replaced ψ1 with V2? (hint: no difficult calculations are required) Check that Ehrenfest's theorem (B&J 3.93) holds for this wavefunction. (d) What...
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