We investigated the quantum states of a free electron with time-dependent effective mass subjected to a time-dependent magnetic field by solving the Schrodinger equation under the choice of Landau and symmetric gauges. Using the invariant operator and unitary transformation methods together, we derived exact wavefunctions of the system. The wavefunctions rely on the solution of associated classical dynamical systems. We confirmed that the quantum analysis of the system under the two gauges coincides mutually.

Exact quantum theory of noninteracting electrons with time-dependent effective mass in a time-dependent magnetic field

A general treatment of the quantal time-dependent coupled oscillators in presence of the variable magnetic field is presented. The treatment is based on the use of an alternative canonical transformations, time-dependent unitary transformations and the invariant methods. Exact wave functions for Schrodinger equations of this system are constructed.We applied our theory to a particular case and, co,sequently, showed that our results recovers to the perviously known one.

An alternative approach to exact wave functions for time-dependent coupled oscillator model of charged particle in variable magnetic field

The dynamics of the time-dependent coupled oscillator model for the motion of a charged particle subjected to a time-dependent external magnetic field is investigated. We use the canonical transformation approach for the classical treatment of the system, whereas the unitary transformation approach is used in managing the system in the framework of quantum mechanics. For both approaches, the original system is transformed into a much more simple system that is the sum of two independent harmonic oscillators with time-dependent frequencies. We therefore easily identify the wavefunctions in the transformed system with the help of an invariant operator of the system. The full wavefunctions in the original system are derived from the inverse unitary transformation of the wavefunctions associated with the transformed system.

http://iopscience.iop.org/article/10.1088/0031-8949/82/06/065004/pdf

The time-dependent coupled oscillator model for the motion of a charged particle in the presence of a time-varying magnetic field

A hybrid approach for quantizing complicated motion of a charged particle in time-varying magnetic field

The kinetic and spectral properties of systems with random mass are considered. The conductivity sigma 0 of an electron gas with random effective mass is calculated in the coherent potential approximation. The authors show that the low-lying long-wave excitations of this system are described by the non-linear matrix sigma -model. The density of states of a two-dimensional electron gas with random mass in a perpendicular strong magnetic field is calculated.

Zh S Gevorkian

Papers

Systems of particles with random mass