TABLE OF CONTENTS I see the atoms, free and fine,
That bubble like a sparkling wine;
I hear the songs electrons sing,
Jumping from ring to outer ring;
Lister The Physicist
Up to now we have been concerned with rather artificial problems. We said: let us assume that the potential energy of our electron varies as a function of distance this way or that way without specifying the actual physical mechanism responsible for it. It was not a waste of time. It gave an opportunity of becoming acquainted with Schr dinger's equation, and of developing the first traces of a physical picture based, perhaps paradoxically, on the mathematical solution.
It would, however, be nice to try our newly acquired technique on a more physical situation where the potential is caused by the presence of some other physical 'object'. The simplest 'object' would be a proton, which, as we know, becomes a hydrogen atom if joined by an electron.
We are going to ask the following questions: (i) What is the probability that the electron is found at a distance r from the proton? (ii) What are the allowed energy levels?
The answers are again provided by Schr dinger's equation. All we have to do is to put in the potential energy due to the presence of a proton and solve the equation.
The wave function is a function of time, and one might want to solve problems, where the conditions are given at t = 0, and one is...
