Results 1 - 10
of
15
The quantum mechanics SUSY algebra: an introductory review
, 2002
"... Starting with the Lagrangian formalism with N = 2 supersymmetry in terms of two Grassmann variables in Classical Mechanics, the Dirac canonical quantization method is implemented. The N = 2 supersymmetry algebra is associated to one-component and two-component eigenfunctions considered in the Schröd ..."
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Cited by 18 (3 self)
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Starting with the Lagrangian formalism with N = 2 supersymmetry in terms of two Grassmann variables in Classical Mechanics, the Dirac canonical quantization method is implemented. The N = 2 supersymmetry algebra is associated to one-component and two-component eigenfunctions considered in the Schrödinger picture of Nonrelativistic Quantum Mechanics. Applications are contemplated.
Supersymmetric Calogero-Moser-Sutherland models: superintegrability structure and aigenfunctions, to appear
- in the proceedings of the Workshop on superintegrability in classical and quantum systems, ed. P Winternitz, CRM series
"... A new generalization of the Jack polynomials that incorporates fermionic variables is presented. These Jack superpolynomials are constructed as those eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland (CMS) model that decomposes triangularly in terms of the ..."
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Cited by 14 (12 self)
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A new generalization of the Jack polynomials that incorporates fermionic variables is presented. These Jack superpolynomials are constructed as those eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland (CMS) model that decomposes triangularly in terms of the symmetric monomial superfunctions. Many explicit examples are displayed. Furthermore, various new results have been obtained for the supersymmetric version of the CMS models: the Lax formulation, the construction of the Dunkl operators and the explicit expressions for the conserved charges. The reformulation of the models in terms of the exchange-operator formalism is a crucial aspect of our analysis.
Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
- SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2009
"... When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the ..."
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Cited by 2 (1 self)
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When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the survey of the results existing in the subject the algebraic and analytic properties of hidden-symmetry differential operators are rigorously elaborated in the Theorems and illuminated by several examples.
On the Geometry of Supersymmetric Quantum Mechanical Systems ∗
, 710
"... We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the considered systems to higher dimensions and more complicated potenti ..."
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Cited by 2 (1 self)
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We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the considered systems to higher dimensions and more complicated potentials. 1
Solutions of the central Woods-Saxon potential in
"... l 6 = 0 case using mathematical modification method ..."
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Relativistic Schrödinger Wave Equation for Hydrogen Atom Using Factorization Method
, 2012
"... In this investigation a simple method developed by introducing spin to Schrödinger equation to study the relativistic hydrogen atom. By separating Schrödinger equation to radial and angular parts, we modify these parts to the associated Laguerre and Jacobi differential equations, respectively. Bound ..."
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In this investigation a simple method developed by introducing spin to Schrödinger equation to study the relativistic hydrogen atom. By separating Schrödinger equation to radial and angular parts, we modify these parts to the associated Laguerre and Jacobi differential equations, respectively. Bound state Energy levels and wave functions of relativistic Schrödinger equation for Hydrogen atom have been obtained. Calculated results well matched to the results of Dirac’s relativistic theory. Finally the factorization method and supersymmetry approaches in quantum mechanics, give us some first order raising and lowering operators, which help us to obtain all quantum states and energy levels for diffe-rent values of the quantum numbers n and m.
in Path Integral Representation
, 2009
"... The first and second Born approximation are studied with the path integral representation for T matrix. The T matrix is calculated for Woods-Saxon potential scattering. To make corresponding integrals solvable analytically, an approximate function for the Woods-Saxon potential is used. Finally it sh ..."
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The first and second Born approximation are studied with the path integral representation for T matrix. The T matrix is calculated for Woods-Saxon potential scattering. To make corresponding integrals solvable analytically, an approximate function for the Woods-Saxon potential is used. Finally it shown that the Born series is converge at high energies and orders higher than two in Born approximation series can be neglected.
and
, 2008
"... The quantization of systems with first- and second-class constraints within the coherentstate path-integral approach is extended to quantum systems with fermionic degrees of freedom. As in the bosonic case the importance of path-integral measures for Lagrange multipliers, which in this case are in g ..."
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The quantization of systems with first- and second-class constraints within the coherentstate path-integral approach is extended to quantum systems with fermionic degrees of freedom. As in the bosonic case the importance of path-integral measures for Lagrange multipliers, which in this case are in general expected to be elements of a Grassmann algebra, is explicated. Several examples with first- and second-class constraints are discussed. 1
