(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The wave function Ψ of a quantum mechanical system described by a Hamiltonian H ̂ can be written as a linear combination of linear combination of Φ1 and Φ2 which are eigenfunctions of H ̂ with eigenvalues E1 and E2 respectively. At t=0, the system is prepared in the state Ψ0=4/5 Φ1+3/5 Φ2 and then allowed to evolve with time. The wave function at time T=1/2 {h/(E1-E2)} will be (accurate within a phase)

a) 4/5 Φ1 + 3/5 Φ2

b) Φ1

c) 4/5 Φ1 - 3/5 Φ2

d) Φ2

e) 3/5 Φ1 + 4/5 Φ2

f) 3/5 Φ1 - 4/5 Φ2

2. Relevant equations

Ψ(x,t) = [itex]\sum[/itex]Cn Φn(x) exp(-i En 2π t/h)

3. The attempt at a solution

I tried evaluate the Ψ for given value of time but couldn't get any relationship between E1 and E2 to simplify it further. I don't know if this approach is right.

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# Homework Help: Quantum Mechanics: Finding Wavefunction

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