SUPERSYMMETRY, VARIATIONAL METHOD AND HULTHEN POTENTIAL

The formalism of supersymmetric quantum mechanics provides us with the eigenfunctions to be used in the variational method to obtain the eigenvalues for the Hulthen potential.

CONTINUED-FRACTION FORMALISM APPLIED TO THE SPIN-1/2 XYZ MODEL

In this paper, we evaluate the correlation functions of the spin-1/2 XYZ model for some particular cases by using the Mori continued-fraction formalism. The results are exactly the same as those well-known ones. This removes any doubt about the convergence of the continued fraction recently raised by some authors.

SUPERSYMMETRIC SOLUTION FOR 2-DIMENSIONAL SCHRODINGER-EQUATION

We use a non usual realization of the superalgebra to resolve certain two-dimensional potentials. The Hartmann and an anisotropic ring-shaped oscillator are explicitly solved.

Solving Schrödinger equation for two dimensional potential using supersymmetry

The formalism of supersymmetric Quantum Mechanics can be extended to arbitrary dimensions. We introduce this formalism and explore its utility to solve the Schodinger equation for a bidimensional potential. This potential can be applied in several systens in physical and chemistry context, for instance, it can be used to study benzene molecule.

Some superstring amplitude computations with the non-minimal pure spinor formalism

We use the non-minimal pure spinor formalism to compute in a super-Poincare covariant manner the four-point massless one and two-loop open superstring amplitudes, and the gauge anomaly of the six-point one-loop amplitude. All of these amplitudes are expressed as integrals of ten-dimensional superfields in a pure spinor superspace which involves five theta coordinates covariantly contracted with three pure spinors. The bosonic contribution to these amplitudes agrees with the standard results, and we demonstrate identities which show how the t(8) and epsilon(10) tensors naturally emerge from integrals over pure spinor superspace.

Supersymmetric quantum mechanics and partially solvable potential

Supersymmetric quantum mechanics can be used to obtain the spectrum and eigenstates of one-dimensional Hamiltonians. It is particularly useful when applied to partially solvable potentials because a superalgebra allows us to compute the spectrum state by state. Some solutions for the truncated Coulomb potential, an asymptotically linear potential, and a nonpolynomial potential are shown to exemplify the method.

BRST-BFV formalism for the generalized Schwinger model

We derive the Wess-Zumino scalar term of the generalized Schwinger model both in the singular and nonsingular cases by using BRST-BFV framework. The photon propagators are also computed in the extended Lorentz gauge.

A generalized Jaynes-Cummings Hamiltonian and supersymmetric shape invariance

A class of shape-invariant bound-state problems which represent two-level systems are introduced. It is shown that the coupled-channel Hamiltonians obtained correspond to the generalization of the Jaynes-Cummings Hamiltonian.

Supersymmetric variational energies for the confined Coulomb system

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. (C) 2002 Elsevier B.V. B.V. All rights reserved.

EXPLICIT SOLUTIONS FOR TRUNCATED COULOMB POTENTIAL OBTAINED FROM SUPERSYMMETRY

The Schrodinger equation with the truncated Coulomb potential is solved using the supersymmetric quantum mechanics formalism, with and without the cutoff in the angular momentum potential. We obtain some analytical eigenfunctions and eigenvalues for particular values of the cutoff parameter.

Geometrical Lagrangian for a supersymmetric Yang-Mills theory on the group manifold

Perhaps one of the main features of Einstein's General Theory of Relativity is that spacetime is not flat itself but curved. Nowadays, however, many of the unifying theories like superstrings on even alternative gravity theories such as teleparalell geometric theories assume flat spacetime for their calculations. This article, an extended account of an earlier author's contribution, it is assumed a curved group manifold as a geometrical background from which a Lagrangian for a supersymmetric N = 2, d = 5 Yang-Mills - SYM, N = 2, d = 5 - is built up. The spacetime is a hypersurface embedded in this geometrical scenario, and the geometrical action here obtained can be readily coupled to the five-dimensional supergravity action. The essential idea that underlies this work has its roots in the Einstein-Cartan formulation of gravity and in the 'group manifold approach to gravity and supergravity theories'. The group SYM, N = 2, d = 5, turns out to be the direct product of supergravity and a general gauge group g: G = g circle times <(SU(2, 2/1))over bar>.

SUPERSYMMETRIC CONSTRUCTION OF W-ALGEBRAS FROM SUPER TODA AND WZNW THEORIES

A systematic construction of super W algebras in terms of the WZNW model based on a super Lie algebra is presented. These are shown to be the symmetry structure of the super Toda models, which can be obtained from the WZNW theory by Hamiltonian reduction. A classification, according to the conformal spin defined by an improved energy momentum tensor, is discussed in general terms for all super Lie algebras whose simple roots are fermionic. A detailed discussion employing the Dirac bracket structure and an explicit construction of W algebras for the cases of OSP(1, 2), OSP(2, 2), OSP(3, 2) and D(2, 1\ alpha) are given. The N = 1 and N = 2 superconformal algebras are discussed in the pertinent cases.

Supersymmetric and shape-invariant generalization for nonresonant and intensity-dependent Jaynes-Cummings systems

A class of shape-invariant bound-state problems which represent transitions in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels as well as intensity-dependent interactions. We show that the coupled-channel Hamiltonians obtained correspond to the generalizations of the nonresonant and intensity-dependent Jaynes-Cummings Hamiltonians, widely used in quantized theories of lasers. In this general context, we determine the eigenstates, eigenvalues, the time evolution matrix and the population inversion matrix factor.

Supersymmetry, variational method and the Lennard-Jones (12,6) potential

The formalism of supersymmetric quantum mechanics is used to determine trial functions in order to obtain eigenvalues for the Lennard-Jones (12, 6) potential from variational method. The superpotential obtained provides an effective potential which can be directly comparable to the original one.

On the quantum Hamilton-Jacobi formalism

Some postulates are introduced to go from the classical Hamilton-Jacobi theory to the quantum one. We develop two approaches in order to calculate propagators, establishing the connection between them and showing the equivalence of this picture with more known ones such as the Schrödinger's and the Feynman's formalisms. Applications of the above-mentioned approaches to both the standard case of the harmonic oscillator and to the harmonic oscillator with time-dependent parameters are made. © 1991 Plenum Publishing Corporation.