FULLY SECOND-QUANTIZED HAMILTONIAN FOR INTERACTING ELECTRONS AND PHONONS,
Abstract
The phonon operators used in describing interacting electron-phonon systems in terms of a secondquantized Hamiltonian Equation (1) are commonly derived from the first-quantized Hamiltonian of the harmonic oscillator, and are therefore not the true creation and annihilation operators of the second-quantized formalism. In this report the multiparticle Schrodinger equation for an electron-ion system is used as the starting point for a derivation of the fully second-quantized Hamiltonian Equation (6), which is expressed in terms of the correct creation and annihilation operators for both electron and phonon fields. The two most significant steps taken in this derivation are the transition from the Schrodinger equation to the corresponding second-quantized Hamiltonian, and the introduction of the true electron and phonon creation and annihilation operators which arise from the expansion of the electron and phonon field operators in appropriate sets of oneparticle wave functions. It is then shown that the conventional phonon operators are equivalent to certain bilinear combinations of the true phonon creation and annihilation operators, at least in the subspace of states having only one particle present in each of the vibrational modes; and the equality of the conventional and of the fully second-quantized Hamiltonians within this subspace of states follows immediately. Finally, it is pointed out that several significant advantages are obtained by using the fully second-quantized Hamiltonian rather than the conventional Hamiltonian in applications of the temperature-dependent double-time Green's function method. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 30, 1964
- Accession Number
- AD0455960
Entities
People
- C. Alton Coulter
- D. W. Howgate
- R. A. Shatas