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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{hbar

^{2}}{ma}[/itex] and [itex]\frac{hbar

^{2}}{4ma}[/itex] and sketch the wave functions.

## Homework Equations

I know there are three parts of the wave function that has the general solution

Ae

^{kx}+ Be

^{-kx}

I also know for -inf to -a the term cancels out leaving only Ae

^{kx}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) Ae

^{kx}

2) Ce

^{kx}+ 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}{hbar

^{2}}[/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{hbar

^{2}}{ma}[/itex] and [itex]\frac{hbar

^{2}}{4ma}[/itex] part.

Sorry I don't know why the fraction code isn't working. It should read (hbar^2)/(ma,4ma)