##### Quantum Physics For Dummies If your quantum physics instructor asks you to solve for the wave function of the center of mass of the electron/proton system in a hydrogen atom, you can do so using a modified Schrödinger equation: What you will find is that you can actually ignore and go straight on to Here’s how it works.

Because the Schrödinger equation contains terms involving either R or r but not both, the form of this equation indicates that it’s a separable differential equation. And that means you can look for a solution of the following form: Substituting the preceding equation into the one before it gives you the following: And dividing this equation by gives you This equation has terms that depend on either but not both. That means you can separate this equation into two equations, like this (where the total energy, E, equals ER + Er): Multiplying gives you And multiplying gives you Now you have two Schrödinger equations, which you can solve independently.

So, using you can now solve for which is the wave function of the center of mass of the electron/proton system. This is a straightforward differential equation, and the solution is Here, C is a constant and k is the wave vector, where In practice, however, ER is so small that people almost always just ignore — that is, they assume it to be 1. In other words, the real action is in is the wave function for the center of mass of the hydrogen atom, and is the wave function for a (fictitious) particle of mass m.