Accession Number : AD0013557


Title :   THE STEADY STATES OF AN ELECTRON IN A PHONON-MODULATED LATTICE


Descriptive Note : Technical rept.


Corporate Author : WASHINGTON STATE UNIV PULLMAN


Personal Author(s) : Band, William


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/013557.pdf


Report Date : 18 May 1953


Pagination or Media Count : 17


Abstract : An electron in a lattice potential together with the phonon mod es of the lattice are treated as a single combined system for which the wave functions are products of Bloch functions for the electron and Hermite polynomial oscillator functions for the normal modes of the lattice vibrations. The classical oscillatory motion of the lattice points is replaced by the probability distributions of the oscillator wave functions, and the modulation of the lattice potential by the phonon modes depends only on the electron position coordinates and on the generalized coordinates of the phonon modes; it does not depend explicitly on the time. Steady resonance states of the combined system, electron plus phonon, are shown to exist in which a single quantum of phonon energy passes back and forth between electron and lattice, the total energy is conserved, and the normalizaiton of the combined eigenfunction is a constant independent of time. The electric current carried in these steady states can have any arbitrary value, and the phonon modulated lattice has absolutely zero resistance. Electrical resistance is considered due to random transitions among the phonon oscillator states of the lattice, stimulated by thermal fluctuations, and the significance of this for the theory of superconductivity is briefly discussed.


Descriptors :   *SOLID STATE PHYSICS , *SUPERCONDUCTIVITY , *QUANTUM THEORY , *PHONONS , PROBABILITY DISTRIBUTION FUNCTIONS , ENERGY , EIGENVECTORS , MOTION , VARIATIONS , ELECTRONS , COORDINATES , RESONANCE , POLYNOMIALS , TRANSITIONS , ELECTRICAL RESISTANCE , ELECTRIC CURRENT , WAVE FUNCTIONS , MODULATION , OSCILLATION , SPECIAL FUNCTIONS(MATHEMATICS) , TIME DEPENDENCE , STIMULATION(GENERAL) , STEADY STATE , THERMAL PROPERTIES , OSCILLATORS


Subject Categories : Solid State Physics


Distribution Statement : APPROVED FOR PUBLIC RELEASE