# Dirac Delta potential

As we know a particle in attractive Dirac delta potential has discontinuity in the derivative of its wavefunction.

I have two questions in this regard:

1. Can a second order differential equation be still defined when the first order derivative is discontinuous at some point?

2. How can we justify $E<0$ for bound state when the particle in an attractive Dirac-delta potential will be confined to a single point?

• A classical particle will be confined to a single point. A wavefunction describing a quantum particle will not. – probably_someone Mar 12 '18 at 5:47