© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Science

THE RUSSIAN ACADEMY OF SCIENCE

James R. Millar, Ann E. Robertson, Daniel H. Kaiser, Louise Mcreynolds, Donald J. Raleigh, Nicholas V. Riasanovsky, Ronald Grigor Suny, Marianna Tax Choldin, Gregory L. Freeze, Paul R. Gregory, Lindsey Hughes, Paul R. Josephson, Janet L. B. Martin, Bruce W. Menning, Boris N. Mironov, Reginald E. Zelnik, James R. Millar

Published Jun 3, 1927• 13 citations

Abstract

A general technique is outlined for investigating supersymmetry properties of a charged spin-1 quantum particle in time-varying electromag-2 netic fields. The case of a time-varying uniform magnetic induction is examined and shown to provide a physical realization of a supersymmetric quantum-mechanical system. Group-theoretic methods are used to factorize the relevant Schrödinger equations and obtain eigensolutions. The quantum behavior of a nonrelativistic charged spin- 1 2 particle in the presence of a constant and uniform magnetic induction is of importance in many physical contexts.

DOI: 10.1126/science.65.1692.538

Related papers

Supersymmetry and a time-dependent Landau system

V. Alan Kostelecký, Vladimir I. Man’ko, Michael Martin Nieto +1 more

A general technique is outlined for investigating supersymmetry properties of a charged spin-1/2 quantum particle in time-varying electromagnetic fields. The case of a time-varying uniform magnetic induction is examined and shown to provide a physical realization of a supersymmetric quantum-mechanical system. Group-theoretic methods are used to factorize the relevant Schr\"odinger equations and obtain eigensolutions. The supercoherent states for this system are constructed.

arXiv:hep-th/9303068•Physical Review A•Aug 1, 1993•34 citations

Supersymmetric Quantum Mechanics and SUSY Dependent SU(2) Symmetry for a Spin-1/2 Charged Particle in a Magnetic Field

Jia Wen-Zhi, Shun-Jin Wang

We find that in a supersymmetric quantum mechanics (SUSY QM) system, in addition to supersymmetric algebra, an associated SU(2) algebra can be obtained by using semiunitary (SUT) operator and projection operator, and the relevant constants of motion can be constructed. Two typical quantum systems are investigated as examples to demonstrate the above finding. The first example is the quantum system of a nonrelativistic charged particle moving in x-y plane and coupled to a magnetic field along z-axis. The second example is provided with the Dirac particle in a magnetic field. Similarly there exists an SU τ (2) ⊗ SU σ (2) symmetry in the context of the relativistic Pauli Hamiltonian squared. We show that there exists also an SU(2) symmetry associated with the supersymmetry of the Dirac particle.

Communications in Theoretical Physics•Aug 1, 2008•2 citations

Quantum behavior of a charged particle in an axial magnetic field

Ashok Das, J. Frenkel, S. H. Pereira +1 more

We study some aspects of the quantum theory of a charged particle moving in a time-independent, unidirectional magnetic field. When the field is uniform, we make a few clarifying remarks on the use of angular momentum eigenstates and momentum eigenstates with the diamagnetism of a free electron gas as an example. When the field is nonuniform but weakly varying, we discuss both perturbative and nonperturbative methods for studying a quantum mechanical system. As an application, we derive the quantized energy levels of a charged particle in a Helmholtz coil, which go over to the usual Landau levels in the limit of a uniform field.

arXiv:hep-th/0404256•Physical Review A•Nov 17, 2004•13 citations

Nonrelativistic spin 1/2 particle in an arbitrary non-Abelian magnetic field in two spatial dimensions

Clark, T E, Love, S T, Nowling, S R

The (group and spin space) matrix Hamiltonian describing the dynamics of a nonrelativistic spin 1/2 particle moving in a static, but spatially dependent, non-Abelian magnetic field in two spatial dimensions is shown to take the form of an anticommutator of a nilpotent operator and its hermitian conjugate. Consequently, the (group space) matrix Hamiltonians for the two different spin projections form partners of a supersymmetric quantum mechanical system. The resulting supersymmetry algebra is exploited to explicitly construct the exact zero energy ground state wavefunction(s) for the system. The remaining eigenstates and eigenvalues of the two partner Hamiltonians form positive energy degenerate pairs.

•Sep 12, 2001•1 citation

Solution of the Schrödinger Equation for Some Electric Field Problems

Lawrence H. Buch, Harry H. Denman

An alternate treatment of the Schrödinger equation for a charged particle in a uniform, constant electric field is given. The time-varying field is then treated. Next, using a Hamiltonian which gives the classical equations of motion for a particle in a viscous medium subject to a uniform constant, or time-varying field, the corresponding Schrödinger equation is solved. This procedure yields the classical electrical conductivity expressions for both dc and ac fields.

American Journal of Physics•Apr 1, 1974•24 citations

Supersymmetric quantum mechanics requires g=2 for vector bosons

Georg Junker

Relativistic arbitrary spin Hamiltonians are shown to obey the algebraic structure of supersymmetric quantum system if their odd and even parts commute. This condition is identical to that required for the exactness of the Foldy-Wouthuysen transformation. Applied to a massive charged spin-1 particle in a constant magnetic field, supersymmetric quantum mechanics necessarily requires a gyromagnetic factor g = 2.

arXiv:2003.11377•Europhysics Letters (EPL)•May 29, 2020•2 citations

A general technique is outlined for investigating supersymmetry properties of a charged spin-1 quantum particle in time-varying electromag-2 netic fields. The case of a time-varying uniform magnetic induction is examined and shown to provide a physical realization of a supersymmetric quantum-mechanical system. Group-theoretic methods are used to factorize the relevant Schrödinger equations and obtain eigensolutions. The quantum behavior of a nonrelativistic charged spin- 1 2 particle in the presence of a constant and uniform magnetic induction is of importance in many physical contexts.

We find that in a supersymmetric quantum mechanics (SUSY QM) system, in addition to supersymmetric algebra, an associated SU(2) algebra can be obtained by using semiunitary (SUT) operator and projection operator, and the relevant constants of motion can be constructed. Two typical quantum systems are investigated as examples to demonstrate the above finding. The first example is the quantum system of a nonrelativistic charged particle moving in x-y plane and coupled to a magnetic field along z-axis. The second example is provided with the Dirac particle in a magnetic field. Similarly there exists an SU τ (2) ⊗ SU σ (2) symmetry in the context of the relativistic Pauli Hamiltonian squared. We show that there exists also an SU(2) symmetry associated with the supersymmetry of the Dirac particle.

We study some aspects of the quantum theory of a charged particle moving in a time-independent, unidirectional magnetic field. When the field is uniform, we make a few clarifying remarks on the use of angular momentum eigenstates and momentum eigenstates with the diamagnetism of a free electron gas as an example. When the field is nonuniform but weakly varying, we discuss both perturbative and nonperturbative methods for studying a quantum mechanical system. As an application, we derive the quantized energy levels of a charged particle in a Helmholtz coil, which go over to the usual Landau levels in the limit of a uniform field.

The (group and spin space) matrix Hamiltonian describing the dynamics of a nonrelativistic spin 1/2 particle moving in a static, but spatially dependent, non-Abelian magnetic field in two spatial dimensions is shown to take the form of an anticommutator of a nilpotent operator and its hermitian conjugate. Consequently, the (group space) matrix Hamiltonians for the two different spin projections form partners of a supersymmetric quantum mechanical system. The resulting supersymmetry algebra is exploited to explicitly construct the exact zero energy ground state wavefunction(s) for the system. The remaining eigenstates and eigenvalues of the two partner Hamiltonians form positive energy degenerate pairs.