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The European Physical Journal Plus

Quantum dynamics of a kicked system with position-dependent effective mass

M. Vubangsi, Martin Tchoffo, Lukong Cornelius Fai

Published Jun 1, 2014• 22 citations
Publisher
DOI
10.1140/epjp/i2014-14129-8

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Abstract The purpose of this work is to reproduce the dynamic of a neutral quantum particle bounded in a conical surface utilizing a position-dependent effective mass background in the non-relativistic regime. We start this task with the construction of the position-dependent effective mass Hamiltonian, containing the effective potential in the Zhou–Kroemer parametrization. We obtain a differential equation for the mass distribution which could reproduce the exact wavefunctions of a scalar quantum particle constrained to a conical space.
Quantum dots, liquid crystals, compositionally graded crystals, and other condensed matter systems all use position dependent effective mass (PDEM) Hamiltonians to describe the dynamics of electrons. Because the PDEM quantum Hamiltonians are not Hermitian, we employ the effective mass kinetic energy operator in Von Ross?s two-parameter form, which is Hermitian by default and contains additional reasonable forms as special instances. It is shown that Hamiltonians of the form H(s)=(1-s)H_-+sH_+,0?s?1 where H_? are supersymmetric partner Hamiltonians corresponding to position dependent mass Schr?dinger equations are exactly solvable for a number of deformed shape invariant potentials.