SUPERSYMMETRIC QUANTUM MECHANICS APPLIED TO NONRELATIVISTIC QUARK MODELS

1993 ◽  
Vol 08 (08) ◽  
pp. 1437-1455 ◽  
Author(s):  
E.J.O. GAVIN ◽  
H. FIEDELDEY ◽  
H. LEEB ◽  
S.A. SOFIANOS
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Approximation Scheme ◽  
Energy Levels ◽  
Supersymmetric Quantum Mechanics ◽  
S Wave ◽  
Nucleon Spectrum ◽  
Quark Potential ◽  
Quark Models ◽  
Original Potential

We examine the effect of changing the energy levels and normalization constants of bound states corresponding to baryons and mesons in nonrelativistic quark models. We do this by applying the transformations of supersymmetric quantum mechanics (SUSYQM) to the potentials used in these models. In particular, we fit the spectra and leptonic decay widths of [Formula: see text] and [Formula: see text] mesons by modifying several existing [Formula: see text] potentials by means of supersymmetric transformations. It is found that the potentials are unchanged beyond 2 fm, and that fitting the widths induces greater oscillations in the potentials than those generated by adjusting the energy levels only. Transformations of SUSYQM are applied to the hypercentral potential in order to accommodate the Roper resonance in the s-wave nucleon spectrum. The quark-quark potential found by inverting the transformed hypercentral potential via a new exact Abel transform differs significantly from the original potential up to 5 fm from the origin and violates the concavity requirement. The [Formula: see text] potential related to this potential by Lipkin’s rule does not reproduce the meson spectrum. As the Hall-Post lower bound is also accurate for baryons, the results of the application of supersymmetric transformations in this approximation scheme are also considered and compared to the upper bound of the hypercentral approximation.

Calculation of energy eigenvalues via supersymmetric quantum mechanics

1989 ◽  
Vol 67 (10) ◽  
pp. 931-934 ◽  
Author(s):  
Francisco M. Fernández ◽  
Q. Ma ◽  
D. J. DeSmet ◽  
R. H. Tipping
Keyword(s):  
Quantum Mechanics ◽  
Ground State ◽  
Potential Energy Function ◽  
Supersymmetric Quantum Mechanics ◽  
Energy Eigenvalues ◽  
Arbitrary Power ◽  
Rational Function Approximation ◽  
Ricatti Equation ◽  
Original Potential ◽  
Ground State Energies

A systematic procedure using supersymmetric quantum mechanics is presented for calculating the energy eigenvalues of the Schrödinger equation. Starting from the Hamiltonian for a given potential-energy function, a sequence of supersymmetric partners is derived such that the ground-state energy of the kth one corresponds to the kth eigen energy of the original potential. Various theoretical procedures for obtaining ground-state energies, including a method involving a rational-function approximation for the solution of the Ricatti equation that is outlined in the present paper, can then be applied. Illustrative numerical results for two one-dimensional parity-invariant model potentials are given, and the results of the present procedure are compared with those obtainable via other methods. Generalizations of the method for arbitrary power-law potentials and for radial problems are discussed briefly.

scholarly journals Variational calculations for the hydrogen-antihydrogen system with a mass-scaled Born-Oppenheimer potential

Open Physics ◽  
2012 ◽  
Vol 10 (5) ◽  
Author(s):  
Henrik Stegeby ◽  
Konrad Piszczatowski ◽  
Hans Karlsson ◽  
Roland Lindh ◽  
Piotr Froelich
Keyword(s):  
Bound States ◽  
Vibrational Energy ◽  
Scattering Length ◽  
Energy Levels ◽  
Nuclear Interaction ◽  
S Wave ◽  
Proton Antiproton ◽  
Mass Scaling ◽  
Variational Calculations ◽  
Vibrational Energy Levels

AbstractThe problem of proton-antiproton motion in the H-$\bar H$ system is investigated by means of the variational method. We introduce a modified nuclear interaction through mass-scaling of the Born-Oppenheimer potential. This improved treatment of the interaction includes the nondivergent part of the otherwise divergent adiabatic correction and shows the correct threshold behaviour. Using this potential we calculate the vibrational energy levels with angular momentum 0 and 1 and the corresponding nuclear wave functions, as well as the S-wave scattering length. We obtain a full set of all bound states together with a large number of discretized continuum states that might be utilized in variational four-body calculations. The results of our calculations gives an indication of resonance states in the hydrogen-antihydrogen system.

Nuclear Physics Methods for Problems in Relativistic Quantum Mechanics

1998 ◽  
Vol 07 (05) ◽  
pp. 559-571
Author(s):  
Marcos Moshinsky ◽  
Verónica Riquer
Keyword(s):  
Quantum Mechanics ◽  
Nuclear Physics ◽  
Bound States ◽  
Relativistic Quantum ◽  
Negative Energy ◽  
Relativistic Quantum Mechanics ◽  
Variational Parameter ◽  
Approximate Methods ◽  
Rest Energy ◽  
Quark Models

Atomic and molecular physicists have developed extensive and detailed approximate methods for dealing with the relativistic versions of the Hamiltonians appearing in their fields. Nuclear physicists were originally more concerned with non-relativistic problems as the energies they were dealing with were normally small compared with the rest energy of the nucleon. This situation has changed with the appearance of the quark models of nucleons and thus the objective of this paper is to use the standard variational procedures of nuclear physics for problems in relativistic quantum mechanics. The 4 × 4α and β matrices in the Dirac equation are replaced by 2 × 2 matrices, one associated with ordinary spin and the other, which we call sign spin, is mathematically identical to the isospin of nuclear physics. The states on which our Hamiltonians will act will be the usual harmonic oscillator ones with ordinary and sign spin and the frequency ω of the oscillator will be our only variational parameter. The example discussed as an illustration will still be the Coulomb problem as the exact energies of the relativistic bound states are available for comparison. A gap of the order of 2mc2 is observed between states of positive and negative energy, that permits the former to be compared with the exact results.

scholarly journals Bound states at threshold in supersymmetric quantum mechanics

1998 ◽  
Vol 515 (1-2) ◽  
pp. 184-202 ◽  
Author(s):  
Massimo Porrati ◽  
Alexander Rozenberg
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Supersymmetric Quantum Mechanics

scholarly journals Bound states in the continuum from supersymmetric quantum mechanics

1993 ◽  
Vol 48 (5) ◽  
pp. 3525-3531 ◽  
Author(s):  
J. Pappademos ◽  
U. Sukhatme ◽  
A. Pagnamenta
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Supersymmetric Quantum Mechanics ◽  
The Continuum

Bound states in continuum of complex potentials generated by supersymmetric quantum mechanics

2002 ◽  
Vol 300 (6) ◽  
pp. 595-602 ◽  
Author(s):  
Jovana S. Petrović ◽  
Vitomir Milanović ◽  
Zoran Ikonić
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Complex Potentials ◽  
Supersymmetric Quantum Mechanics

SUPERSYMMETRY APPROACHES TO THE BOUND STATES OF THE GENERALIZED WOODS–SAXON POTENTIAL

2004 ◽  
Vol 19 (08) ◽  
pp. 615-625 ◽  
Author(s):  
H. FAKHRI ◽  
J. SADEGHI
Keyword(s):  
Differential Equation ◽  
Quantum Mechanics ◽  
Bound States ◽  
Differential Operators ◽  
Energy Levels ◽  
Negative Energy ◽  
Saxon Potential ◽  
First Order ◽  
Jacobi Differential Equation ◽  
Algebraic Solutions

Using the associated Jacobi differential equation, we obtain exactly bound states of the generalization of Woods–Saxon potential with the negative energy levels based on the analytic approach. According to the supersymmetry approaches in quantum mechanics, we show that these bound states by four pairs of the first-order differential operators, represent four types of the laddering equations. Two types of these supersymmetry structures, suggest the derivation of algebraic solutions by two different approaches for the bound states.

BOUND STATES FOR SCHRÖDINGER HAMILTONIANS: PHASE SPACE METHODS AND APPLICATIONS

1996 ◽  
Vol 08 (04) ◽  
pp. 503-547 ◽  
Author(s):  
PH. BLANCHARD ◽  
J. STUBBE
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Dynamical Systems ◽  
Bound States ◽  
Energy Levels ◽  
Schrödinger Operators ◽  
Particle Systems ◽  
Existence And Nonexistence ◽  
Phase Space Methods ◽  
Special Case

Properties of bound states for Schrödinger operators are reviewed. These include: bounds on the number of bound states and on the moments of the energy levels, existence and nonexistence of bound states, phase space bounds and semi-classical results, the special case of central potentials, and applications of these bounds in quantum mechanics of many particle systems and dynamical systems. For the phase space bounds relevant to these applications we improve the explicit constants.

ANOMALOUS SUSY QUANTUM MECHANICS, HETEROTIC MODELS AND SCATTERING STATES

1992 ◽  
Vol 07 (25) ◽  
pp. 2325-2331
Author(s):  
L. J. BOYA ◽  
J. CASAHORRÁN ◽  
J. G. ESTEVE
Keyword(s):  
Quantum Mechanics ◽  
Symmetry Breaking ◽  
Continuous Spectrum ◽  
Real Axis ◽  
Bound States ◽  
Anomalous Behavior ◽  
Heterotic String ◽  
Supersymmetric Quantum Mechanics ◽  
The Other ◽  
Scattering States

We analyze the symmetry breaking associated to anomalous realization of supersymmetry in the context of Supersymmetric Quantum Mechanics (SUSY QM). We show how the supercharge itself might become an anomalous operator in the process of quantization. We study a solvable potential in the Pöschl-Teller class containing both bound states and continuous spectrum. We find a situation reminiscent of the heterotic string: one of the two SUSY partners lives in the whole real axis while the other restricts itself to the half-line. Peculiarities of the model include negative energies, incomplete pairing of states and anomalous behavior for the phase shifts in scattering.

scholarly journals SECOND ORDER DERIVATIVE SUPERSYMMETRY, q DEFORMATIONS AND THE SCATTERING PROBLEM

1995 ◽  
Vol 10 (18) ◽  
pp. 2683-2702 ◽  
Author(s):  
A.A. ANDRIANOV ◽  
M.V. IOFFE ◽  
F. CANNATA ◽  
J.-P. DEDONDER
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Scattering Amplitude ◽  
Scattering Problem ◽  
Higher Order ◽  
Supersymmetric Quantum Mechanics ◽  
Self Similarity ◽  
Systematic Analysis ◽  
Higher Derivative ◽  
Reflectionless Potential

In a search for pairs of quantum systems linked by dynamical symmetries, we give a systematic analysis of novel extensions of standard one-dimensional supersymmetric quantum mechanics. The most general supercharges involving higher order derivatives are introduced, leading to an algebra which incorporates a higher order polynomial of the Hamiltonian. We investigate the condition for irreducibility of such a higher order generator to a product of standard first derivative Darboux transformations. As a new example of application of this approach we study the quantum-mechanical radial problem including the scattering amplitudes. We also investigate the links between this higher derivative SUSY and a q-deformed supersymmetric quantum mechanics and introduce the notion of self-similarity in momentum space. An explicit model for the scattering amplitude is constructed in terms of a hypergeometric function which corresponds to a reflectionless potential with infinitely many bound states.

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