npsm 새물리 New Physics : Sae Mulli

pISSN 0374-4914 eISSN 2289-0041
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New Phys.: Sae Mulli 2020; 70: 1112-1116

Published online December 31, 2020 https://doi.org/10.3938/NPSM.70.1112

Copyright © New Physics: Sae Mulli.

Landau States in Time-Dependent Magnetic Fields

Won KIM1, Sang Pyo KIM2,3*

1Department of Physics, Kunsan National University, Kunsan 54150, Korea

2Department of Physics, Kunsan National University, Kunsan 54150, Korea
3Center for Relativistic Laser Science, Institute for Basic Science, Gwangju 34126, Korea

Correspondence to:sangkim@kunsan.ac.kr

Received: September 28, 2020; Revised: October 13, 2020; Accepted: October 23, 2020

Abstract

We present the oscillator representation of the Pauli Hamiltonian for a scalar charge in a magnetic field and find a basis that diagonalizes the Hamiltonian in the special case of a constant or slowly varying magnetic field. We show that the diagonalization of the new basis is a canonical transformation in phase space, which leads to the Pauli Hamiltonian and counts the degeneracy of the Landau levels. Finally, we obtain the Liouville-von Neumann equation for quantum invariants as the annihilation and the creation operators for a scalar charge in time-dependent magnetic fields.

Keywords: Landau levels, Time-dependent magnetic field, Quantum invariants, Time-dependent annihilation and creation operators

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