QM beginner's question about deltafunction potential problem

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runninglow
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how can i know the number of boundstate of a particle acting under a deltafunction potential?
 
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Or if you want to go the whole nine

1) Write Schrödinger's equation
2) Solve Schrödinger's equation with the appropriate boundary conditions (Psi continuous at x=0, dPsi/dx discontinuous by a certain amount), and the condition that E<0
3) Show that there is in fact only one such state