Can I get explanation for you choice please or detailed solution!! At t = 0, a H

Question

Can I get explanation for you choice please or detailed solution!!

At t = 0, a Harmonic Oscillator with mass m and classical angular frequency omega is in the state Psi = 1/Squareroot 2 (u_0 (x) - u_1 (x)), where u_n is the nth energy eigenstate of the HO. What is the wavefunction at a later time t? Psi = 1/Squareroot 2 (u_0 (x)e^-i omega t - u_1 (x)e^-3i omega t) Psi = 1/Squareroot 2(u_0 (x) - u_1 (x)) Psi = 1/Squareroot 2 (u_0 (x) - u_1 (x))e^i omega t Psi = 1/Squareroot 2 (u_0 (x) - u_1 (x)e^-i omega t)e^-i omega t/2 none of the above

Explanation / Answer

At later time t,

wave function=wave function at t=0*exp(-i*E*t/hcross)

E is the energy.

En=hcross*w*(n+1/2)

E0=hcross*w/2

E1=3*hcross*w/2

So, wave function at time t

=(1/2)*(u0(x)*exp(-i*hcross*w*t/(2*hcross))-u1(x)*exp(-i*3*hcross*w*t/(2*hcross)))

So, correct option is d.

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