Bound-state perturbation method via SVZ sum rules in quantum mechanics

1985 ◽  
Vol 35 (10) ◽  
pp. 1067-1083 ◽  
Author(s):  
I. Novák ◽  
Š. Olejník
Keyword(s):  
Quantum Mechanics ◽  
Perturbation Method ◽  
Sum Rules ◽  
Bound State

Bound state solution of the Schrodinger equation for the Woods–Saxon potential plus coulomb interaction by Nikiforov–Uvarov and supersymmetric quantum mechanics methods

2021 ◽  
pp. 2150023
Author(s):  
Enayatolah Yazdankish
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Interaction ◽  
Schrodinger Equation ◽  
Energy Eigenvalue ◽  
Bound State ◽  
Repulsive Interaction ◽  
Saxon Potential ◽  
Special Cases ◽  
Supersymmetry Quantum Mechanics

The generalized Woods–Saxon potential plus repulsive Coulomb interaction is considered in this work. The supersymmetry quantum mechanics method is used to get the energy spectrum of Schrodinger equation and also the Nikiforov–Uvarov approach is employed to solve analytically the Schrodinger equation in the framework of quantum mechanics. The potentials with centrifugal term include both exponential and radial terms, hence, the Pekeris approximation is considered to approximate the radial terms. By using the step-by-step Nikiforov–Uvarov method, the energy eigenvalue and wave function are obtained analytically. After that, the spectrum of energy is obtained by the supersymmetry quantum mechanics method. The energy eigenvalues obtained from each method are the same. Then in special cases, the results are compared with former result and a full agreement is observed. In the [Formula: see text]-state, the standard Woods–Saxon potential has no bound state, but with Coulomb repulsive interaction, it may have bound state for zero angular momentum.

scholarly journals LORENTZ BOOSTED NN POTENTIAL FOR FEW-BODY SYSTEMS: APPLICATION TO THE THREE-NUCLEON BOUND STATE

2003 ◽  
Vol 18 (02n06) ◽  
pp. 124-127 ◽  
Author(s):  
H. KAMADA ◽  
W. GLÖCKLE ◽  
J. GOLAK ◽  
CH. ELSTER
Keyword(s):  
Quantum Mechanics ◽  
Binding Energy ◽  
Schrodinger Equation ◽  
Relativistic Quantum ◽  
Bound State ◽  
Nucleon Nucleon ◽  
Relativistic Quantum Mechanics ◽  
Equal Time ◽  
Momentum Change ◽  
Approximate Scheme

In the context of equal time relativistic quantum mechanics we introduce a Lorentz boosted potential. The dynamical input are nonrelativistic realistic nucleon-nucleon (NN) potentials, which by a suitable momentum change are analytically transformed into NN potentials fulfilling the relativistic two-nucleon Schrödinger equation in the c.m. system. The binding energy of the three nucleon (3N) bound state is calculated and we find that the boost effects for the two-body subsystems are repulsive and lower the binding energy. In addition we compare to a recently proposed approximate scheme.

scholarly journals Systematic errors of bound-state parameters obtained with SVZ sum rules

2007 ◽  
Author(s):  
Wolfgang Lucha ◽  
Dmitri Melikhov ◽  
Silvano Simula ◽  
Pietro Colangelo ◽  
Donato Creanza ◽  
...  
Keyword(s):  
Sum Rules ◽  
Systematic Errors ◽  
Bound State

THE MASSLESS BOUND STATE FORMALISM IN TWO-PARTICLE RELATIVISTIC QUANTUM MECHANICS

1988 ◽  
Vol 03 (05) ◽  
pp. 1235-1261 ◽  
Author(s):  
H. SAZDJIAN
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Three Dimensional ◽  
Bound State ◽  
Relativistic Quantum Mechanics ◽  
Composite Systems ◽  
Bound State Case ◽  
State Case

We develop, in the framework of two-particle relativistic quantum mechanics, the formalism needed to describe massless bound state systems and their internal dynamics. It turns out that the dynamics here is two-dimensional, besides the contribution of the spin degrees of freedom, provided by the two space-like transverse components of the relative coordinate four-vector, decomposed in an appropriate light cone basis. This is in contrast with the massive bound state case, where the dynamics is three-dimensional. We also construct the scalar product of the theory. We apply this formalism to several types of composite systems, involving spin-0 bosons and/or spin-1/2 fermions, which produce massless bound states.

THE MASS OF A QUARK–SQUARK BOUND STATE FROM QCD SUM RULES

1999 ◽  
Vol 14 (30) ◽  
pp. 4763-4780
Author(s):  
M. MEYER-HERMANN ◽  
A. SCHÄFER
Keyword(s):  
Sum Rules ◽  
Mass Range ◽  
Bound State ◽  
Higher Order ◽  
Qcd Sum Rules ◽  
Mass Effects ◽  
Squark Mass

We give an estimate of the expected mass range for a possible two-quark two-squark bound state, using QCD sum rules. The sum rules are modified, taking mass effects into account, so that a treatment of heavy squarks becomes justified. The influence of the higher-order mass corrections and the possibility of a bound state mass below the squark mass are discussed.

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