The exact bound-state ansaetze as zero-order approximations in perturbation theory I. The formalism and padé oscillators

1991 ◽  
Vol 41 (5) ◽  
pp. 397-408 ◽  
Author(s):  
M. Znojil
Keyword(s):  
Perturbation Theory ◽  
Bound State ◽  
Zero Order ◽  
Exact Bound

Exact bound-state solutions of the cut-off Coulomb potential inN-dimensional space

Pramana ◽  
1992 ◽  
Vol 39 (5) ◽  
pp. 493-499 ◽  
Author(s):  
R N Chaudhuri ◽  
M Mondal
Keyword(s):  
Coulomb Potential ◽  
Dimensional Space ◽  
Bound State ◽  
Exact Bound

EXACT SOLUTIONS OF DIRAC EQUATION FOR A NEW SPHERICALLY ASYMMETRICAL SINGULAR OSCILLATOR

2010 ◽  
Vol 25 (33) ◽  
pp. 2849-2857 ◽  
Author(s):  
GUO-HUA SUN ◽  
SHI-HAI DONG
Keyword(s):  
Dirac Equation ◽  
Vector Potential ◽  
State Energy ◽  
Energy Levels ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Exact Bound ◽  
Spinor Wave

In this work we solve the Dirac equation by constructing the exact bound state solutions for a mixing of scalar and vector spherically asymmetrical singular oscillators. This is done provided that the vector potential is equal to the scalar potential. The spinor wave functions and bound state energy levels are presented. The case V(r) = -S(r) is also considered.

On the choice of the zero-order operator in perturbation theory

1972 ◽  
Vol 17 (2) ◽  
pp. 303-305 ◽  
Author(s):  
Th. Hoffmann-Ostenhof ◽  
F. Mark
Keyword(s):  
Perturbation Theory ◽  
Zero Order ◽  
Order Operator

Integral equations and exact solutions for the fourth Painlevé equation

1992 ◽  
Vol 437 (1899) ◽  
pp. 1-24 ◽  
Keyword(s):  
Integral Equations ◽  
Inverse Scattering ◽  
Bound State ◽  
Painlevé Equation ◽  
Exact Bound ◽  
Painleve Equation ◽  
Linear Integral ◽  
Dnls Equation ◽  
Special Case ◽  
Linear Integral Equations

We consider a special case of the fourth Painlevé equation given by d 2 ƞ / dξ 2 = 3 ƞ 5 + 2ξ ƞ 3 + (1/4ξ 2 - v - 1/2 ) ƞ , (1) with v a parameter, and seek solutions ƞ (ξ; v ) satisfying the boundary condition ƞ (∞)=0. (2) Equation (1) arises as a symmetry reduction of the derivative nonlinear Schrödinger (DNLS) equation, which is a completely integrable soliton equation solvable by inverse scattering techniques. Solutions of equation (1), satisfying (2), are expressed in terms of the solutions of linear integral equations obtained from the inverse scattering formalism for the DNLS equation. We obtain exact ‘bound state’ solutions of equation (1) for v = n , a positive integer, using the integral equation representation, which decay exponentially as ξ→ ± ∞ and are the first example of such solutions for the Painlevé equations. Additionally, using Bäcklund transformations for the fourth Painlevé equation, we derive a nonlinear recurrence relation (commonly referred to as a Bäcklund transformation in the context of soliton equations) for equation (1) relating ƞ (ξ; v ) and ƞ (ξ; v + 1).

BINDING ENERGIES IN WEAKLY COUPLED (2+1)-DIMENSIONAL QUANTUM FIELD THEORIES

1991 ◽  
Vol 06 (29) ◽  
pp. 2705-2711
Author(s):  
G. GAT ◽  
B. ROSENSTEIN
Keyword(s):  
Perturbation Theory ◽  
Binding Energy ◽  
Bound State ◽  
Binding Energies ◽  
Field Theories ◽  
General Question ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Weakly Coupled ◽  
Gross Neveu Model

We calculate the binding energy of the two-particle threshold bound state in the (2+1)-dimensional Gross-Neveu model. This model was recently shown to be renormalizable within the 1/N expansion. The binding energy is found to be ΔE=4mc-8Nf where m is the mass of the elementary fermion and Nf is the number of flavors. The general question of consistency of the perturbation theory within the framework of the Bethe-Salpeter equation is discussed.

Expansion in angular momenta in bound-state perturbation theory

1956 ◽  
Vol 233 (1195) ◽  
pp. 527-536 ◽  
Keyword(s):  
Perturbation Theory ◽  
Relativistic Electron ◽  
Bound State ◽  
Static Potential ◽  
Heavy Atoms ◽  
Angular Momenta

An expansion of the propagator S F (F) (x 2 , x 1 ) of a relativistic electron in a central static potential is given. The terms of this expansion correspond to the angular momenta of the electron propagated by this function. Applications to problems concerning heavy atoms are indicated.

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