Supersymmetric quantum mechanics

Crombrugghe, M. de; Rittenberg, V.

doi:10.1016/0003-4916(83)90316-0

Cited by 308 publications

(274 citation statements)

References 16 publications

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“…This quantum system is known to possess an N = 2 supersymmetry [7,8], and one may exploit this supersymmetry to find for instance the exact zero-energy ground-state wavefunctions of the system in the presence of an arbitrary, spatially dependent, magnetic field [9,10]. In this paper we shall generalize the N = 2 supersymmetry property of the Pauli Hamiltonian to the case when the underlying two-dimensional manifold is a curved surface.…”

Section: Introductionmentioning

confidence: 99%

Supersymmetry-Based Approach to Quantum Particle Dynamics on a Curved Surface with Non-zero Magnetic Field

Kim

Lee

2002

Annals of Physics

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We present the N = 2 supersymmetric formulation for the classical and quantum dynamics of a nonrelativistic charged paritcle on a curved surface in the presence of a perpendicular magnetic field. For a particle moving on a constant-curvature surface in a constant magnetic field, our Hamiltonian possesses the shape-invariance property in addition. On the surface of a sphere and also on the hyperbolic plane, we exploit the supersymmetry and shape-invariance properties to obtain complete solutions to the corresponding quantum mechanical problems. *

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Section: Introductionmentioning

confidence: 99%

Supersymmetry-Based Approach to Quantum Particle Dynamics on a Curved Surface with Non-zero Magnetic Field

Kim

Lee

2002

Annals of Physics

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“…The generators Q α and the Casimir operator C = Q α η αβ Q β = 3 8 (SΠ − Π 2 ) of this algebra form also s(2, 1) superalgebra [24],…”

Section: Revealing Dynamical (Super)symmetriesmentioning

confidence: 99%

Pseudoclassical model for topologically massive gauge fields

Nirov

Plyushchay

1998

J. High Energy Phys.

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A pseudoclassical model for P ,T -invariant system of topologically massive U(1) gauge fields is analyzed. The model demonstrates a nontrivial relationship between continuous and discrete symmetries and reveals a phenomenon of "classical quantization". It allows one to identify SU(1,1) symmetry and S(2,1) supersymmetry as hidden symmetries of the corresponding quantum system. We show this P ,T -invariant quantum system realizes an irreducible representation of a non-standard super-extension of the (2 + 1)-dimensional Poincaré group.

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“…Now motivated by the work of Ramos and Roca, let us perform the change of variable described by 3) and concentrate on the latter two equations in (5.2). These become…”

Section: Ugr-covariant Lax Operatormentioning

confidence: 99%

“…Almost sixty years later the mathematical setting for this class of theories was established [2]. Finally one-hundred and fifty years later, explorations of the connection between supersymmetry and integrable systems began in earnest [3,4]. The topic of integrable systems has also been found to coalesce with relativistic particle and spinning particles [5] in an unexpected way wherein the KdV and SKdV Lax operators can be found by use of an appropriate set of variables [6].…”

Section: Introductionmentioning

confidence: 99%