The hydrogen atom and the classical theory of radiation

Extract

The paper considers the application of Dirac's classical theory of radiating electrons to consider the straight line motion of an electron towards a fixed proton and the straight line motion of two oppositely charged electrons. The paper also gives a discussion of the probable solutions in two- and three-dimensional motions of an electron moving round a fixed proton. In all these cases there appears to be no solution which would permit a collision between the two particles.

I take this opportunity to express my deepest gratitude to Prof. Dirac for his patient guidance and supervision, and also to Christ's College for a scholarship.

Note added. In the problem of the rectilinear motion considered in section (2), if we take the charges on the particles to be of like signs, then we find that the equations of motion have a solution which corresponds to a collision. In place of equation (4) we have

It can be easily verified that under suitable initial conditions there is a solution with x→0 and y→∞. Near x=0 the solution is approximately . Thus a collision is possible for like charges and not possible for unlike charges. The result, in both cases, is the opposite of what we should expect from elementary physical considerations.