# Visualization of a time-dependent Potential

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.)