Exact solution of the Schrödinger equation for the movement of a particle in a parametric magnetic field
DOI:
https://doi.org/10.33448/rsd-v10i7.16401Keywords:
Schrödinger's Equation; Time-dependent quadratic system; Spatio-temporal transformation; Mathieu equation and functions; Resonance and parametric oscillations.Abstract
We solved the Schrödinger equation exactly for a time-dependent quadratic system for a particle that moves under the influence of a magnetic field with parametric oscillation. We apply the decoupling method, which adopts a transformation of Ray-Reid's spatio-temporal coordinates (Nassar, 1990). The fundamental idea of the problem is to obtain a Schrödinger free particle equation. In this way, it was possible to determine the wave function and the probability density of the particle in the form of a parametric vibration function. We show that the regions of stability and instability are determined by the phase space defined by the equation's control parameters. We determined, as an unprecedented result, the discrete values that the magnetic field can assume in terms of Mathieu functions.
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Copyright (c) 2021 João Bosco Soares Pampolha Junior; Charles da Rocha Silva; João Paulo da Silva Alves; Renato Germano; Damião Pedro Meira Filho
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