# Jumps between energy states of harmonic oscillators

I have recently read that in perfect harmonic oscillators to go up or down in energy state you have to go, using the simile of a staircase, step by step, emitting or absorbing a photon of energy $$E=\hbar\omega$$ where w is the frequency of the oscillator. . But molecules are not perfect harmonic oscillators, and I have doubts about Planck's development of his blackbody radiation emission law. When Planck says that the energy emitted or absorbed by an oscillator is a multiple of $$\hbar \omega$$, he means that it absorbs/emits several photons of energy $$E=\hbar\omega$$ or that it can emit/absorb photons of energy $$\hbar \omega, \ 2\hbar \omega, \ 3\hbar \omega\dots$$ Using the simile of the staircase, can Planck oscillators go up/down two steps at a time, or three or four...?

Thank you for your time.

## 1 Answer

Yes, electrons/atoms/molecules can skip steps if they absorb energy that is equal to the gap between some state and another, higher energy state.

In the more realistic case of anharmonic oscillators the energy gaps get closer as they get higher.

For some molecules the harmonic oscillator is a good approximation for vibration, especially for a homo-diatom like $$O_2$$. Other atomic bonds also behave like harmonic oscillator around the ground state, and this approximation is used in all atom molecular dynamics (simulating the classical behavior of molecules) to model the bonds between atoms.

It is a good approximation, but like any other approximation it has its limits.

• Just a nitpick, but not “all” simulations use harmonic force fields. Some use ab initio forces from quantum calculations, which can be post-harmonic. Aug 31, 2023 at 19:36
• Yeah, my bad. I actually meant all-atom and not all MD simulations. Aug 31, 2023 at 20:33