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Временная динамика волновых функций электронов трехмерного квантового кольца в переменном магнитном поле

Александр Анатольевич Брызгалов, F. I. Karmanov

Published Jan 1, 2011• 0 citations
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Abstract

Three-dimensional axially symmetrical exactly soluble model of quantum ring has been considered in the constant magnetic field. Potential, which restricts particle movement in the system in two directions, has been used. By applying method of splitting into physical processes, an electron wave functions and a quasi-stationary energy levels values have been obtained. Also a qualitative description of wave packet movement has been given for the case of quantum ring threading by alternating magnetic field.

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Three-dimensional axially symmetrical exactly soluble model of quantum ring has been considered in the constant magnetic field. Potential, which restricts particle movement in the system in two directions, has been used. By applying method of splitting into physical processes, an electron wave functions and a quasi-stationary energy levels values have been obtained. Also a qualitative description of wave packet movement has been given for the case of quantum ring threading by alternating magnetic field.
Three-dimensional axially symmetrical exactly soluble model of quantum ring has been considered in the constant magnetic field. Potential, which restricts particle movement in the system in two directions, has been used. By applying method of splitting into physical processes, an electron wave functions and a quasi-stationary energy levels values have been obtained. Also a qualitative description of wave packet movement has been given for the case of quantum ring threading by alternating magnetic field.
The generalized Duffin–Kemmer equation for a spin 1 particle with the anomalous magnetic moment in the external uniform magnetic field is investigated. The separation of variables in the wave equation is performed on the basis of projective operator techniques. The problem is reduced to a system of differential equations for three independent functions that have been solved in terms of the confluent hypergeometric functions. Three series of the energy levels are found. To assign them the physical sense at all values of the main quantum number n = 0,1, 2, , special restrictions on anomalous magnetic moment values must be imposed – they are formulated in explicit form. Otherwise, only some part of the energy levels corresponds to the bound states. The neutral spin 1 particle is considered as well. In this case, no bound states exist in the systems. The main qualitative manifestation of the anomalous magnetic moment is the space scaling of the arguments of the wave functions in comparison with a particle without such a moment.
A)A new beam-splitter on the basement of coherent scattering of two-and three-level atom in the field of standing amplitude-modulated waves is investigated. A detailed study of three cases of amplitude modulation of practical importance is presented: harmonic modulation, triangle pulse modulation and «meander» modulation. It is demonstrated that for all the three regimes it is possible to choose such an amplitude and modulation frequency that the coherent component amplitude with defined values of the atom pulses is essentially increased. The influence of the initial phase on the character of wave packet scattering has been also investigated.
Based on the method of V-function, a continuation of the optical-mechanical analogy is attained. In contrast to classic quantum mechanics, a trajectory-wave motion of the particle is explored. We highlight the presence of energy quantization of the particle and the availability of solution without a particle in the case of rectilinear uniform motion at constant speed. A solution to the direct and inverse problems of dynamics is searched for in a new statement for a hydrogen-like atom. When solving a direct problem, we find a stationary wave function of the electron in a hydrogen-like atom, with its properties investigated. When searching for a final solution to the stationary wave equation, we take into account a solution to the inverse problem of dynamics for the electron. A linear dependence between two particular solutions is shown. The second linearly independent solution is found, decaying exponentially to zero. We present charts of the stationary solution for a wave of the particle (electron) for three lower stationary states. Energy levels of a hydrogen-like atom are determined as a solution to the inverse problem of dynamics, which fully coincide with the classical results by Schrödinger and Bohr. A wave function is regarded as a physical reality, which makes it possible to open up new possibilities in order to study the structure of the microcosm