The connection between the strictly isospectral construction in supersymmetric quantum mechanics and the general zero mode solutions of the Schroedinger equation is explained by introducing slightly generalized first-order intertwining operators. We also present a multiple-parameter generalization of the strictly isospectral construction in the same perspective.

The evolution of single-particle energies with varying isospin asymmetry in the shell model is an important issue when predicting changes in the shell structure for exotic nuclei. In many cases pseudospin partner levels, that are almost degenerate in energy for stable nuclei, are relevant in extracting the size of the shell gaps. A breaking of the pseudospin symmetry can affect the size of thes...

Using supersymmetric quantum mechanics we develop a new method for constructing quasi-exactly solvable (QES) potentials with two known eigenstates. This method is extended for constructing conditionally-exactly solvable potentials (CES). The considered QES potentials at certain values of parameters become exactly solvable and can be treated as CES ones.

Stochastic quantization is applied to derivation of the equations for the Wilson loops and generating functionals of the Wilson loops in the N = ∞ limit. These equations are treated both in the coordinate and momentum representations. In the first case the connection of the suggested approach with the problem of random closed contours and supersymmetric quantum mechanics is established, and the...

We propose a general method that allows to detect the existence of normalizable ground states in supersymmetric quantum mechanical systems with non-Fredholm spectrum. We apply our method to show the existence of bound states at threshold in two important cases: 1) the quantum mechanical system describing H-monopoles; 2) the quantum mechanics of D0 branes. e-mail [email protected] Permanen...

Supersymmetric quantum mechanics is formulated on a two dimensional noncommutative plane and applied to the supersymmetric harmonic oscillator. We find that the ordinary commutative supersymmetry is partially broken and only half of the number of supercharges are conserved. It is argued that this breaking is closely related to the breaking of time reversal symmetry arising from noncommutativity.

We explicitly construct a solution of eight-dimensional gauged supergravity representing D6-branes wrapped on six-cycles inside Calabi–Yau fourfolds. The solution preserves two supercharges and asymptotically is a cone with the coset space SU(2)/U(1) as its base. It is shown to correspond to an M-theory compactification on a Calabi–Yau manifold with SU(5) holonomy and we discuss in detail its g...

We advocate a set of approximations for studying the finite temperature behavior of strongly-coupled theories in 0+1 dimensions. The approximation consists of expanding about a Gaussian action, with the width of the Gaussian determined by a set of gap equations. The approximation can be applied to supersymmetric systems, provided that the gap equations are formulated in superspace. It can be ap...

The methodology based on the association of the Variational Method with Supersymmetric Quantum Mechanics is used to evaluate the energy states of the confined hydrogen atom.

This is an elem&ary introduction to the classical and quantum mechanics of a single bosonic string, and to some aspects of its supersymmetric and heterotic extensions1