EFFECTIVE-MASS THEORY FOR POLARONS IN EXTERNAL FIELDS

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 [p+(ec)A]22mpol, where mpol is the polaron effective mass. Likewise, for a slowly varying potential V(r), the effective Hamiltonian describing the polaron motion is P22mpol+V(r) for those states in which the polaron momentum remains small. No explicit assumptions about the strength of the electron-LO coupling are made. © 1969 The American Physical Society.