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## Homework Statement

A particle moves in one dimension in the delta function potential V= αδ(x). (where that is an 'alpha' ... not 'a')

An initial wave function is given

[tex] \Psi = A(a^2-x^2) [/tex] for x between -a and a and Psi=0 anywhere else

What is the probability that an energy measurement will yield something other than:

[tex] E=\frac{-m\alpha^2}{2\hbar^2} [/tex]

note: when we solve the delta function potential problem, we find (for E<0) that there is only one bound state, and only one allowed energy: and that is exactly the one shown above.

## Homework Equations

[tex] c_n = \int \Psi_n^* \Psi(x,0) dx[/tex]

[tex] P(E_n) = abs(c_n)^2 [/tex]

## The Attempt at a Solution

At first I was sure that since there is only one bound state in the delta function potential problem, and only one allowed energy, that the probability of measuring another energy should be zero. But when I calculate the coefficient c1, I do not get 1, i get something like .913 and then c1 squared is about .83 which would then be the probability of measuring the bound state energy.

This is what is confusing me. If c1 is not equal to 1, then there must be some other c's with other eigenfunctions that must be combined linearly to produce the given initial wave function. But there is only one energy eigenfunction, so what are these other functions??

And if there is only one energy eigenstate, is it possible to measure an energy other than the energy of the eigenstate?

Thank you