Time dependent problem with a delta function

[Paul159]

Hello,

I try to solve a time dependent problem described by a Hamiltonian of the type $$ \mathcal{H}(t) = H_0 + V \delta(t) .$$

I started by trying to solve the Schrödinger equation with $H_0 = p^2 / 2m$, but I'm getting a bit stuck.

I would like to know if you know of any books that deal with this kind of problem?

Thank you in advance.

 

[eljose79]

Hello,

Thank you for reaching out with your question. The type of Hamiltonian you are dealing with is known as a Dirac delta potential, and it can be quite tricky to solve. One book that I would recommend for understanding this type of problem is "Quantum Mechanics: Non-Relativistic Theory" by L.D. Landau and E.M. Lifshitz. Chapter 9 specifically deals with the Dirac delta potential and provides a detailed explanation and solution to the problem.

Another useful resource is "Introduction to Quantum Mechanics" by David J. Griffiths, which also covers the Dirac delta potential in Chapter 2. Both of these books are commonly used in undergraduate and graduate level quantum mechanics courses and should provide a solid foundation for understanding and solving your problem.

I hope this helps and good luck with your research!