What are some examples of systems with time-dependent Hamiltonians?

[diegzumillo]

Hi all!
I'm starting to study the time evolution operator, and now i came up with this objective... i need a time dependant hamiltonian! since no fundamental interaction is time dependent i need to think of a system in such a configuration that i have a time dependency on H.
Anyway, if anyone has any idea i'd be very happy to discuss them! :D

 

[lbrits]

Not fundamental, but effective: An electron in a rotating magnetic field:
$$\mathbf{B}(t) = sin(\omega t) \mathbf{x} + \cos(\omega t) \mathbf{y}$$

 

[denian]

Hello! It's great to hear that you are studying the time evolution operator. As you mentioned, it is true that no fundamental interaction is time dependent. However, there are systems in which the Hamiltonian can vary with time. One example is a system that is subject to external forces, such as an electron in an electromagnetic field. In this case, the Hamiltonian will depend on the time-varying electric and magnetic fields.

Another example is a system undergoing a phase transition, where the Hamiltonian can change as the system moves through different phases. This can be seen in the study of superconductors, where the Hamiltonian changes as the temperature of the system changes.

I also suggest looking into systems with time-dependent boundary conditions, such as a particle in a moving potential well. In this case, the Hamiltonian will vary as the potential well moves, leading to a time-dependent Hamiltonian.

I hope these examples give you some ideas to explore. Best of luck with your studies!