On the Derivation and the Properties of an Effective Hamiltonian for a Polaron in an External Magnetic Field

✍ Scribed by J. Röseler; K. Henneberger; H. J. Fischbeck

• Publisher: John Wiley and Sons
• Year: 1973
• Tongue: English
• Weight: 476 KB
• Volume: 55
• Category: Article
• ISSN: 0370-1972
• DOI: 10.1002/pssb.2220550215

✦ Synopsis

Abstract

The lowest eigenvalues of Frohlich's Hamiltonian with a magnetic field are approximately determined by solving the eigenvalue problem of an effective Hamiltonian for a polaron in a magnetic field. The effective Hamiltonian can be diagonalized without approximations, and the eigenvalue problem is reduced to the determination of the energy‐momentum relation of a free polaron. In the present paper it is shown in which manner the effective Hamiltonian can be derived from Frohlich's Hamiltonian with a magnetic field. The approximations being necessary for this derivation are justified on the condition ω~c~/ω~0~ = |e| · |B|/m c ω~0~ ≪ 1 in the case of weak and intermediate coupling. Furthermore, the properties of the eigen‐value spectrum belonging to the effective Hamiltonian are discussed.