Ladder operators can be constructed for all potentials that present the integrability condition known as shape invariance, satisfied by most of the exactly solvable potentials. Using the superalgebra of supersymmetric quantum mechanics we construct the ladder operators for two exactly solvable potentials that present a subtle hidden shape invariance. PACS No. 03.65.Fd, 11.30.Pb, 31.15.Pf

Using the supersymmetric quantum mechanics we investigate the wave function-sensitive properties of the supersymmetric potentials which have received a lot of attention in the literature recently. We show that a su-perdeep potential and its phase-equivalent shallow-partner potential give very similar rms values for the weakly bound systems such as the deuteron and 11 Be nuclei. Although the cor...

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 prove the uniqueness of the ground state for a supersymmetric quantum mechanical system of two fermions and two bosons, which is closely related to the N = 1 WZ-model. The proof is constructive and gives detailed information on what the ground state looks like.

A thorough analysis of the general features of (p = 2) parasupersymmetric quantum mechanics is presented. It is shown that for both Rubakov{Spiridonov and Beckers{Debergh formulations of (p = 2)-parasupersymmetric quantum mechanics, the de eneracy structure of the energy spectrum can be derived using the deening parasuperalgebras. Thus the results of the present article is independent of the de...

Using the formalism of supersymmetric quantum mechanics, we obtain a large number of new analytically solvable one-dimensional periodic potentials and study their properties. More specifically, the supersymmetric partners of the Lamé potentials ma(a+ 1) sn(x,m) are computed for integer values a = 1, 2, 3, .... For all cases (except a = 1), we show that the partner potential is distinctly differ...

For the class of central potentials possessing a finite number of bound states and for which the second derivative of rV (r) is negative, we prove, using the supersymmetric quantum mechanics formalism, that an increase of the angular momentum l by one unit yields a decrease of the number of bound states of at least one unit: Nl+1 ≤ Nl − 1. This property is used to obtain, for this class of pote...

Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. If applied to the harmonic oscillator, a family of Hamiltonians ruled by polynomial Heisenberg algebras is obtained. In this paper it will be shown that the SUSY partner Hamiltonians of the harmonic oscillator can produce evolution loops. The corresponding geometric...

We discuss some possible relationships in gauge theories, string theory and M theory in the light of some recent results obtained in gauge invariant supersymmetric quantum mechanics. In particular this reveals a new relationship between the gauge group E8 and 11-dimensional space. PACS: 11.25.-w, 11.25.Mj

The Biedenharn approach to the Dirac-Coulomb problem is applied to a system considered by D'Hoker and Vinet, which consists of a spin 1 2 particle in the combined field of a Dirac monopole plus a λ 2 /r 2 potential. The explicit solution is obtained by diagonalizing the 'Biedenharn-Temple operator', Γ. 1. Introduction. In a paper anticipating supersymmetric quantum mechanics, [1], Biedenharn pr...