Quasi-exactly solvable Hamiltonians: a new approach and an approximation scheme

2003 ◽  
Vol 317 (1-2) ◽  
pp. 46-53 ◽  
Author(s):  
Rajneesh Atre ◽  
Prasanta K. Panigrahi
Keyword(s):  
Approximation Scheme ◽  
New Approach ◽  
Exactly Solvable ◽  
Exactly Solvable Hamiltonians

scholarly journals SUSUSY Quantum Mechanics

1997 ◽  
Vol 12 (01) ◽  
pp. 171-176 ◽  
Author(s):  
David J. Fernández C.
Keyword(s):  
Quantum Mechanics ◽  
Shift Operator ◽  
Second Order ◽  
Parametric Family ◽  
First Order ◽  
Shift Operators ◽  
Exactly Solvable ◽  
Exactly Solvable Hamiltonians

The exactly solvable eigenproblems in Schrödinger quantum mechanics typically involve the differential "shift operators". In the standard supersymmetric (SUSY) case, the shift operator turns out to be of first order. In this work, I discuss a technique to generate exactly solvable eigenproblems by using second order shift operators. The links between this method and SUSY are analysed. As an example, we show the existence of a two-parametric family of exactly solvable Hamiltonians, which contains the Abraham–Moses potentials as a particular case.

scholarly journals INTEGRAL TRANSFORM TECHNIQUE FOR MESON WAVE FUNCTIONS

1996 ◽  
Vol 11 (20) ◽  
pp. 1611-1626 ◽  
Author(s):  
A.P. BAKULEV ◽  
S.V. MIKHAILOV
Keyword(s):  
Wave Function ◽  
Sum Rules ◽  
Integral Transform ◽  
Wave Functions ◽  
Sum Rule ◽  
New Approach ◽  
Exactly Solvable ◽  
The Stability ◽  
The Masses ◽  
Integral Transform Technique

In a recent paper1 we have proposed a new approach for extracting the wave function of the π-meson φπ(x) and the masses and wave functions of its first resonances from the new QCD sum rules for nondiagonal correlators obtained in Ref. 2. Here, we test our approach using an exactly solvable toy model as illustration. We demonstrate the validity of the method and suggest a pure algebraic procedure for extracting the masses and wave functions relating to the case under investigation. We also explore the stability of the procedure under perturbations of the theoretical part of the sum rule. In application to the pion case, this results not only in the mass and wave function of the first resonance (π′), but also in the estimation of π″-mass.

scholarly journals New quasi-exactly solvable Hamiltonians in two dimensions

1994 ◽  
Vol 159 (3) ◽  
pp. 503-537 ◽  
Author(s):  
Artemio González-López ◽  
Niky Kamran ◽  
Peter J. Olver
Keyword(s):  
Two Dimensions ◽  
Exactly Solvable ◽  
Exactly Solvable Hamiltonians

QUASI-EXACTLY SOLVABLE PROBELMS OF QUANTUM MECHANICS AND sl(2)-SYMMETRIC GAUDIN MODEL

1990 ◽  
Vol 05 (23) ◽  
pp. 1883-1889 ◽  
Author(s):  
T. I. MAGLAPERIDZE ◽  
A. G. USHVERIDZE
Keyword(s):  
Quantum Mechanics ◽  
Exact Solutions ◽  
Separation Of Variables ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Gaudin Model ◽  
New Approach ◽  
Completely Integrable ◽  
Partial Separation ◽  
Exactly Solvable

We propose a new approach to the problem of quasi-exact solubility in quantum mechanics. We show that the quasi-exactly solvable Schrödinger equations (allowing exact solutions only for limited parts of the spectrum) can be obtained from the completely integrable Gaudin equation by means of partial separation of variables.

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