QM beginner's question about deltafunction potential problem

[runninglow]

how can i know the number of boundstate of a particle acting under a deltafunction potential?

[Vanadium 50]

Draw the wavefunction. How many ways are there to do this?

[nicksauce]

Or if you want to go the whole nine

1) Write Schrodinger's equation
2) Solve Schrodinger'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