- #1
petera88
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Homework Statement
Given the delta function -α[δ(x+a) + δ(x-a)] where α and a are real positive constants.
How many bound states does it possess? Find allowed energies for [itex]\frac{hbar2}{ma}[/itex] and [itex]\frac{hbar2}{4ma}[/itex] and sketch the wave functions.
Homework Equations
I know there are three parts of the wave function that has the general solution
Aekx + Be-kx
I also know for -inf to -a the term cancels out leaving only Aekx and for x to inf the only term left is some Fe-kx since it can't blow up as x goes to infinity.
The Attempt at a Solution
I set up the three parts of the wave function.
1) Aekx
2) Cekx + De-kx
3) Fe-kx
I also took the derivatives and will use the fact that they will subtract to give me [itex]\frac{-2ma}{hbar2}[/itex]
I know if I solve for k I can get the energy. Honestly I am kind of lost in the understanding of this problem. Especially the [itex]\frac{hbar2}{ma}[/itex] and [itex]\frac{hbar2}{4ma}[/itex] part.
Sorry I don't know why the fraction code isn't working. It should read (hbar^2)/(ma,4ma)