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Finding the full wave equation

I have been stuck on this problem for a while now, and I keep going in vircles, I feel slightly retarded because it seems pretty trivial, anyways I would really appreciate some help.

It is a past exam question:
in this part of the question I am asked to construct the fill wave funxtion with boundary conditions:
ψ(x,t)=12(ψ0(x)+ψ2(x))\psi(x,t) = \frac{1}{\sqrt{2}} (\psi_{0}(x)+\psi_{2}(x))
where before I showed that
Ψ(x,t)=∑cn(t)ψn(x)[br]\Psi(x,t) = \sum c_n(t) \psi_n(x) [br]for
cn(t)=c0(0)e−iℏEnt c_n(t) = c_0(0)e^{\frac{-i}{\hbar}E_nt} and En=(n+12)ℏω E_n = (n+ \frac{1}{2}) \hbar \omega

And it says: to this end show that cn(t)=0 c_n(t) = 0 unless n=0,2 n = 0,2

Constructing the full wave function I can do, but I struggle with showing that n can only be 0, 2!
What I have been trying so far was just playing around with the formulas normalizing it, using eulers identity etc. But its all pretty pointless I keep getting the same thing back.

I'd really appreciate some help!
(edited 9 years ago)
Reply 1
Avatar for Seaam
Seaam
OP
anyone :frown:?
Reply 2
Avatar for Seaam
Seaam
OP
nevermind, problem solved, it was indeed incredibly trivial! :redface:
Pleeeeeease, I didn't read anything except the wave, are you a surfer??????????? Dude


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