# Delta potential

1. Dec 23, 2011

### hokhani

consider a particle in one dimention. there is a dirac delta potential such as V=-a delat(x)
the wave functions in two sides(left and right) are Aexp(kx) and Aexp(-kx) respectively.
so the differential of the wave functions are not continious at x=0. what is the justification here?

Last edited: Dec 23, 2011
2. Dec 23, 2011

Staff Emeritus
Good question. What do you think the answer might be? What is the meaning of the derivative of the wavefunction?

3. Dec 23, 2011

### hokhani

it is a criterion of the momentum and maybe they have opposite momentum. but i can't understand it exactly. i just know that one of the boundary conditions is the continuity of the differential of wave function!!!!!!!

Last edited: Dec 23, 2011
4. Dec 23, 2011

Staff Emeritus
If you want me to help, I will. But you're going to have to work with me. Write in proper English, and don't scream at me by putting a bunch of exclamation points at the end.

Go back a step - what is the physical meaning of the derivative of the wavefunction?

5. Dec 23, 2011

### hokhani

ok. excuse me
i think the derivative of a wave function gives the momentum.

6. Dec 23, 2011

Staff Emeritus
OK, good. Now, what's the derivative dp/dx of momentum?

7. Dec 23, 2011

### hokhani

i think it is the kinetic energy of the particle.

8. Dec 23, 2011

Staff Emeritus
No, it's not, but you're close. Let's come at it from a different direction - I think I'm confusing you. And please write in correct English. Capital letters, punctuation, the whole thing.

You say that the derivative of the wavefunction is momentum, and you are worried that the momentum is discontinuous. What would it mean if the momentum as a function of position were not continuous?

9. Dec 24, 2011

### hokhani

sorry for my English and thank you for pointing that out.
my idea is that when the momentum direction is changed, we have a collision.

10. Dec 24, 2011

### hokhani

Another problem:
Here the momentum operator P has complex eigenvalues while P is a Hermitian operator.

11. Dec 24, 2011