# Conceptual understanding of the Quantum Harmonic oscillator

First: When we consider a quantum particle in a harmonic (quadratic) potential we say that this particle is a harmonic oscillator, because it behaves like one. Is this correct?

Now let us assume our particle is in the groundstate $$\mid \psi_0 \rangle$$. This would mean that in this picture it would be described by the lowest wave with energy $$E_0$$.

I have a bit of a hard time to understand what happens when we increase the energy of said particle. The old wave function disappears and we find our particle in a new state $$\mid \psi_n\rangle$$ with some new energy $$E_n$$ described by a new wave in the picture. Is that correct?

Honestly, I'm giving a presentation on this topic soon, and want to visualize such a 'jump' from a lower energy state to a higher energy state of a particle in the harmonic potential, in the correct way.

Any help is greatly appreciated!

• If you're giving a presentation, it might be safe to say: we know the initial state, and we know the final state, and what happens in between is everything--c.f. Feynman's path integral interpretation. – JEB Feb 22 at 22:53
• Haha, this might be a good starting point the thing is I actually would like to visualize it with pictures. It doesn't have to be 100% correct just close enough that the professors will just nod and think to themselves 'close enough' I a picture like the one I found here ok ? arxiv.org/abs/1708.00749 (page 2) (I am talking about the small harmonic oscillators where a 'dot' which represents a particle jumps from a low energy state to higher energy state. – CatoMaths Feb 22 at 23:16