An Alternative Method for Calculating Bound-State of Energy Eigenvalues of Klein–Gordon for Quasi-exactly Solvable Potentials

2009 ◽  
Vol 26 (2) ◽  
pp. 020302 ◽  
Author(s):  
Eser Olgar
Keyword(s):  
Bound State ◽  
Energy Eigenvalues ◽  
Solvable Potentials ◽  
Alternative Method ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Klein Gordon

scholarly journals RATIONALLY EXTENDED SHAPE INVARIANT POTENTIALS IN ARBITRARY D DIMENSIONS ASSOCIATED WITH EXCEPTIONAL Xm POLYNOMIALS

2017 ◽  
Vol 57 (6) ◽  
pp. 477 ◽  
Author(s):  
Rajesh Kumar Yadav ◽  
Nisha Kumari ◽  
Avinash Khare ◽  
Bhabani Prasad Mandal
Keyword(s):  
Canonical Transformation ◽  
Bound State ◽  
Invariance Property ◽  
Shape Invariance ◽  
Point Canonical Transformation ◽  
Solvable Potentials ◽  
Shape Invariant ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Exceptional Orthogonal Polynomials

Rationally extended shape invariant potentials in arbitrary D-dimensions are obtained by using point canonical transformation (PCT) method. The bound-state solutions of these exactly solvable potentials can be written in terms of <em>X<sub>m</sub></em> Laguerre or <em>X<sub>m</sub></em> Jacobi exceptional orthogonal polynomials. These potentials are isospectral to their usual counterparts and possess translationally shape invariance property.

SUPERSYMMETRIC APPROACH TO QUASINORMAL MODES

2008 ◽  
Vol 23 (10) ◽  
pp. 751-760
Author(s):  
T. K. JANA ◽  
P. ROY
Keyword(s):  
Gordon Equation ◽  
Quasinormal Modes ◽  
Outgoing Wave ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Klein Gordon ◽  
Wave Boundary ◽  
Klein Gordon Equation ◽  
Supersymmetric Approach

Supersymmetry (SUSY) in quantum mechanics is extended from square integrable states to those satisfying the outgoing wave boundary condition. Using this formalism we obtain new exactly solvable potentials admitting quasinormal modes (QNM) solutions of the Klein–Gordon equation.

scholarly journals BOUND STATE WAVE FUNCTIONS THROUGH THE QUANTUM HAMILTON–JACOBI FORMALISM

2004 ◽  
Vol 19 (19) ◽  
pp. 1457-1468 ◽  
Author(s):  
S. SREE RANJANI ◽  
K. G. GEOJO ◽  
A. K. KAPOOR ◽  
P. K. PANIGRAHI
Keyword(s):  
Wide Class ◽  
Bound State ◽  
Wave Functions ◽  
Singularity Structure ◽  
State Wave ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Jacobi Formalism ◽  
Momentum Function

The bound state wave functions for a wide class of exactly solvable potentials are found by utilizing the quantum Hamilton–Jacobi formalism of Leacock and Padgett. It is shown that, exploiting the singularity structure of the quantum momentum function, until now used only for obtaining the bound state energies, one can straightforwardly find both the eigenvalues and the corresponding eigenfunctions. After demonstrating the working of this approach through a few solvable examples, we consider Hamiltonians, which exhibit broken and unbroken phases of supersymmetry. The natural emergence of the eigenspectra and the wave functions, in both unbroken and the algebraically nontrivial broken phase, demonstrates the utility of this formalism.

The quasi-exactly solvable potentials method applied to the three-body problem

2007 ◽  
Vol 322 (5) ◽  
pp. 1034-1042 ◽  
Author(s):  
F. Chafa ◽  
A. Chouchaoui ◽  
M. Hachemane ◽  
F.Z. Ighezou
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Three Body

scholarly journals SPECTRUM OF THE RELATIVISTIC PARTICLES IN VARIOUS POTENTIALS

2005 ◽  
Vol 20 (12) ◽  
pp. 911-921 ◽  
Author(s):  
RAMAZAN KOÇ ◽  
MEHMET KOCA
Keyword(s):  
Quantum Mechanics ◽  
Hypergeometric Functions ◽  
Two Dimensions ◽  
Dirac Oscillator ◽  
Confluent Hypergeometric Functions ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Nonrelativistic Quantum Mechanics ◽  
Relativistic Particles

We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials become exactly and quasi-exactly solvable potentials of nonrelativistic quantum mechanics when they are transformed into a Schrödinger-like equation. For the exactly solvable potentials, eigenvalues are calculated and eigenfunctions are given by confluent hypergeometric functions. It is shown that, our formulation also leads to the study of those potentials in the framework of the supersymmetric quantum mechanics.

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