Why Must ψ and Its Derivative Be Continuous and Finite in Quantum Physics?

[quantumevo]

Hello all,

I have a quantum physics question which is more conceptual and mathematical than anything. Here's the question:

Explain why ψ and its derivative have to be continuous and finite.

 

[gabbagabbahey]

Hi quantumevo, welcome to PF!

We're not here to do your homework for you.

What are your thoughts on the question?...Some things you may want to look at are what the Schroedinger equation looks like at points where the wavefunction is discontinuous; and the probability of measuring the position of a particle in the immediate vicinity of a discontiuity in its wavefunction...