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

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 Exactly solvable charged dilaton gravity theories in two dimensions

1998 ◽  
Vol 15 (10) ◽  
pp. 2973-2979 ◽  
Author(s):  
Youngjai Kiem ◽  
Chang-Yeong Lee ◽  
Dahl Park
Keyword(s):  
Two Dimensions ◽  
Dilaton Gravity ◽  
Exactly Solvable ◽  
Gravity Theories

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.

Superintegrable Systems: Polynomial Algebras and Quasi-Exactly Solvable Hamiltonians

1995 ◽  
Vol 243 (1) ◽  
pp. 144-168 ◽  
Author(s):  
P. Letourneau ◽  
L. Vinet
Keyword(s):  
Polynomial Algebras ◽  
Exactly Solvable ◽  
Superintegrable Systems ◽  
Exactly Solvable Hamiltonians

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 ASPECTS OF EXACTLY SOLVABLE QUANTUM-CORRECTED 2D DILATON GRAVITY THEORIES

1994 ◽  
Vol 09 (04) ◽  
pp. 475-498 ◽  
Author(s):  
ADEL BILAL
Keyword(s):  
Canonical Formalism ◽  
Functional Integral ◽  
Two Dimensions ◽  
Positive Energy ◽  
Dilaton Gravity ◽  
Integral Measure ◽  
Exactly Solvable ◽  
Solvable Quantum ◽  
Gravity Theories ◽  
Selection Of

After reviewing the basic aspects of the exactly solvable quantum-corrected dilaton gravity theories in two dimensions, we discuss a (subjective) selection of other aspects: (a) supersymmetric extensions, (b) the canonical formalism, ADM mass and the functional integral measure, and (c) a positive energy theorem and its application to the ADM and Bondi masses.

scholarly journals Capillary-induced deformations of a thin elastic sheet

2016 ◽  
Vol 374 (2066) ◽  
pp. 20150169 ◽  
Author(s):  
N. D. Brubaker ◽  
J. Lega
Keyword(s):  
Finite Thickness ◽  
Three Dimensional ◽  
Two Dimensions ◽  
System Of Equations ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Drop Volume ◽  
Exactly Solvable ◽  
Encapsulation Process

We develop a three-dimensional model for capillary origami systems in which a rectangular plate has finite thickness, is allowed to stretch and undergoes small deflections. This latter constraint limits our description of the encapsulation process to its initial folding phase. We first simplify the resulting system of equations to two dimensions by assuming that the plate has infinite aspect ratio, which allows us to compare our approach to known two-dimensional capillary origami models for inextensible plates. Moreover, as this two-dimensional model is exactly solvable, we give an expression for its solution in terms of its parameters. We then turn to the full three-dimensional model in the limit of small drop volume and provide numerical simulations showing how the plate and the drop deform due to the effect of capillary forces.

scholarly journals Deformed shape invariance and exactly solvable Hamiltonians with position-dependent effective mass

2005 ◽  
Vol 38 (13) ◽  
pp. 2929-2945 ◽  
Author(s):  
B Bagchi ◽  
A Banerjee ◽  
C Quesne ◽  
V M Tkachuk
Keyword(s):  
Effective Mass ◽  
Shape Invariance ◽  
Exactly Solvable ◽  
Exactly Solvable Hamiltonians
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