Connection between Cartesian and polar wave functions of a nonrelativistic charged particle in a homogeneous magnetic field

A linear transformation is found between the Cartesian and polar wave functions of a nonrelativistic charged particle moving in a homogeneous magnetic field. It is shown that the coefficients of this linear transformation coincide with the normalized Hermite functions $\overline H_n(y_0/a)$, where $y_0=a^2p_x/\hbar$, $p_x$ is the projection of the momentum, and $a$ is a parameter with the dimensions of a length characteristic of the investigated problem.