Effective-Mass Theory for Polarons in External Fields

Abstract

Polaron effective-mass wave functions are constructed which diagonalize approximately the Fröhlich Hamiltonian describing a polaron in a weak magnetic field or in a static external potential which varies slowly in space. In this way it is shown that for low-lying states and in weak magnetic fields, polaron energy levels are eigenvalues of the Hamiltonian $\frac{{[\mathrm{p}+(\frac{e}{c}\left)\mathrm{A}\right]}^2}{2m_{\mathrm{pol}}}$, where $m_{\mathrm{pol}}$ is the polaron effective mass. Likewise, for a slowly varying potential $V\left(\mathrm{r}\right)$, the effective Hamiltonian describing the polaron motion is $\frac{{\mathrm{P}}^2}{2m_{\mathrm{pol}}}+V\left(\mathrm{r}\right)$ for those states in which the polaron momentum remains small. No explicit assumptions about the strength of the electron-LO coupling are made.