to
. As there are two periodic characteristics of the orbit, the general quantum-theory will give two conditions that the orbit must fulfil, instead of only one. It is impossible to explain the process by which the results are obtained, but the results themselves are fairly simple.
The first quantum condition is very much the same as in the case of circular orbits. Take the mass of the electron, its velocity at
(where it is nearest to the nucleus
), and the circumference of the circle whose radius is
, and multiply these three together; the result must be an exact multiple of