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