Exercise 1: Time-dependent Schrödinger equation
Given a time-dependent one-dimensional quantum harmonic oscillator defined by the Hamiltonian
22 H=pˆ +(qˆ−q0(t)) ;
22
with q0(t) = t/T and t ∈ [0 : T]. Given |ψ0⟩ = |n = 0⟩ (ground state of the Harmonic oscillator), compute |ψ(t)⟩ for different values of T. Plot the square norm of |ψ(t)⟩ as a function of q at different times, and the average position of the particle as a function of t.
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