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daleklama
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Homework Statement
This is a Quantum Physics problem.
An electron moves in a one-dimensional potential well such that the potential V = 0 for |x| ≤ a, and V = ∞ otherwise.
The system has energy eigenfunctions:
Un = a^(-1/2) cos (n∏x/2a), for n odd, and
Un = a^(-1/2) sin (n∏x/2a) for n even.
(Those are both for |x| ≤ a)
and Un = 0 for |x| > a.
The lowest energy level of the system is 37.6 eV.
At t=0, the wavefunction for the system is
ψ(x, t = 0) = a^(-1/2) (2 cos (∏x/2a) + sin (∏x/a)).
(1) Write the wavefunction as a linear combination of energy eigenfunctions, and hence normalise the wavefunction.
(2) What are the possible results of a measurement of electron energy?
Homework Equations
Not really sure!
The Attempt at a Solution
Okay, so I think I have 1) complete. The wavefunction as a linear combination of energy eigenfunctions is ψ = 2u1 + u2.
Also, I normalised it and got ψ (norm) = ψ/√5. I'm pretty sure I understand all this.
My problem is with (2). I know that the possible results of an energy measurement are either u1 or u2.
And u1 = E1 = 37.6 eV (given in question)
But I don't understand how to get E2. Apparently E2 = 4 (E1)?? Why would that be true.. I don't understand where that 4 came from? :/
Sorry, I'm an absolute beginner to Quantum Physics so I'm going very very slowly!
Any help would be appreciated :)