Polaron in a Magnetic Field

A study is made of the energy spectrum of a polaron in the presence of a magnetic field for the cases of weak and intermediate couplings, using Onsager's theory. This theory makes use of the Bohr-Sommerfeld quantization rule, which has been derived with the WKB approximation and is therefore valid for large quantum numbers. Following an approach first formulated by Argyres, we prove that the energy spectrum of a polaron in a magnetic field obtained by using Onsager's theory is correct even for small quantum numbers like $n=0, 1, 2$, etc.