scholarly journals QUANTUM HAMILTON–JACOBI ANALYSIS OF PT SYMMETRIC HAMILTONIANS

2005 ◽  
Vol 20 (17) ◽  
pp. 4067-4077 ◽  
Author(s):  
S. SREE RANJANI ◽  
A. K. KAPOOR ◽  
P. K. PANIGRAHI
Keyword(s):  
Time Reversal ◽  
Pt Symmetry ◽  
Complex Domain ◽  
Eigenvalues And Eigenfunctions ◽  
Solvable Potentials ◽  
Exactly Solvable Potentials ◽  
Exactly Solvable ◽  
Jacobi Formalism

We apply the quantum Hamilton–Jacobi formalism, naturally defined in the complex domain, to complex Hamiltonians, characterized by discrete parity and time reversal (PT) symmetries and obtain their eigenvalues and eigenfunctions. Examples of both quasi-exactly and exactly solvable potentials are analyzed and the subtle differences, in the singularity structures of their quantum momentum functions, are pointed out. The role of the PT symmetry in the complex domain is also illustrated.

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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