(a) Show that satisfies the time-dependent Schrdinger equation for the harmonic oscillator potential (Equation 2.44). Here is...

(a) Show that

satisfies the time-dependent Schrödinger equation for the harmonic oscillator potential (Equation 2.44). Here is any real constant with the dimensions of length.
(b) Find |Ψ (x, t)|², and describe the motion of the wave packet.
(c) Compute (x) and (P), and check that Ehrenfest’s theorem (Equation 1.38) is satisfied.

Transcribed Image Text:

1* p [ 201² ( x² + 2 (1 + ²) + the exp 2ħ m y (x, t) = (1751) mo 1/4 -jast 2xore-