My questions come from reading this paper about charging quantum particles.

We have a quantum particle in a harmonic potential which we will charge using a cyclic unitary processes.

Cyclic in this context means that our Hamiltonian

$$H(t) = H_0 + V(t)$$

consists of a time independent component $H_0$ and an applied external time-dependent potential $V(t)$ which is only non-zero in a certain time interval. This means in total that

$$H(0) = H(\tau) = H_0$$

or in other words after the field $V(t)$ has been applied the Hamiltonian returns to its initial state.

Now I am giving a presentation about this topic and would like to visualize this process, but am somewhat unsure as to how to show $V(t)$ acting on the system.

The paper (I provided the link for above) tries to show this on page 8 but I am unsure as to how 'valid' this is.

Maybe to be more exact: Is it possible to show a particle in a harmonic potential, described as a wave-function in the ground state $\mid \psi_0 \rangle$ like in this picture, then show 'some external field acting on this particle' and then show the particle to be in a higher energy state?

Or does anyone else have an idea how to show such a cyclic process acting on a particle in a presentation? (Does not have to be 100% exact, the professor said he prefers clarity over being exact.)


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.