Supersymmetric Quantum Mechanical Systems Research Articles

On the Nicolai map and Witten index for two-dimensional supersymmetric magnetic field systems

Various aspects of two-dimensional supersymmetric quantum mechanical systems with magnetic fields are studied. In particular, Nicolai maps are obtained and an associated stochastic interpretation in terms of a Markovian process with non-potential forces is given. The evaluation of the Witten index in both the heat kernel and resolvent regularisation scheme is considered. An explicit calculation of a specific model is presented, clarifying how the non-integer value of the index is built up.

Supersymmetric path integration

The kernel of the evolution operator for the supersymmetric square root of the Schrödinger equation of a supersymmetric quantum mechanical system is expressed as an integral in the space of paths in superspace. The measure is defined so that the superchange rather than the hamiltonian is fundamental. It is shown that the odd and even parts of the paths in superspace are components of a single superpath. The Fourier mode expansion of the superpath is derived.

New exact solutions of the non-polynomial oscillator [formula omitted] and supersymmetry

It is shown that the non-polynomial oscillator has supersymmetric character and using supersymmetric quantum mechanics we find new exact (analytical) solutions of the non-polynomial oscillator. It is also shown that the new solutions as well as the old ones correspond to ground states of different supersymmetric quantum mechanical systems. mechanical systems.

Tunnel determinants

Methods for computing the regularized determinants of fluctuation operators are being developed. The results follow from the fact that these determinants can be expressed by eigenmodes of the fluctuation operator. As an application the tunnel determinants of some one- and higher-dimensional models are computed. It is shown that every fluctuation operator defines a supersymmetric quantum mechanical system.

Accidental degeneracies and supersymmetric quantum mechanics

Some recently given examples of accidental degeneracies are shown to arise from an underlying supersymmetry. The appropriate dynamical supersymmetries are identified. The relevant spectrum-generating superalgebras for these supersymmetric quantum-mechanical systems are introduced and studied.

Supersymmetric Quantum Mechanics in Three-Dimensional Space. I: One-Particle System with Spin-Orbit Potential

As a direct generalization of the model of supersymmetric quantum mechanics· by Witten, which describes the motion of a spin one·half particle in the one·dimensional space, we construct a model of the supersymmetric quantum mechanics in the three·dimensional space, which describes the motion of a spin one· half particle in central and spin· orbit potentials in the context of the nonrelativistic quantum mechanics. With the simplest choice of the (super) potential, this model is shown to reduce to the model of the harmonic oscillator plus constant spin· orbit potential of unit strength of both positive and negative signs, which was studied in detail in our recent paper in connection with accidental degeneracy as well as the graded groups. This simplest model is discussed in some detail as an example of the three­ dimensional supersymmetric quantum mechanical system, where the supersymmetry is an exact symmetry of the system. More general choice of a polynomial superpotential is also discussed. It is shown that the supersymmetry cannot be spohtaneously broken for any polynomial superpotential in our three-dimen· sional model; this result is contrasted to the corresponding one in the one·dimensional model.