Inverse problem of quantum mechanics for attractive potentials. The discrete spectrum

1984 ◽  
Vol 59 (3) ◽  
pp. 603-608 ◽  
Author(s):  
V. B. Gostev ◽  
A. R. Frenkin
Keyword(s):  
Inverse Problem ◽  
Quantum Mechanics ◽  
Discrete Spectrum

Reply to Comment on 'Inverse problem from the discrete spectrum in the D = 2 dimensional space'

2022 ◽  
Author(s):  
Roland Lombard ◽  
Rabia Yekken
Keyword(s):  
Inverse Problem ◽  
Discrete Spectrum ◽  
Dimensional Space

Abstract We want to thank our colleague F. Fernandez for his interest and his careful reading of our paper "The inverse problem from discrete spectrum in the D = 2 dimensional space". We are confused to have left a number of mistakes in the manuscript.

scholarly journals Pseudo-Hermitian quantum mechanics with unbounded metric operators

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120050 ◽  
Author(s):  
Ali Mostafazadeh
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Discrete Spectrum ◽  
Metric Operator ◽  
Hamiltonian Operators

I extend the formulation of pseudo-Hermitian quantum mechanics to η + -pseudo-Hermitian Hamiltonian operators H with an unbounded metric operator η + . In particular, I give the details of the construction of the physical Hilbert space, observables and equivalent Hermitian Hamiltonian for the case that H has a real and discrete spectrum and its eigenvectors belong to the domain of η + and consequently .

New situation in quantum mechanics (wonderful potentials from the inverse problem)

1997 ◽  
Vol 13 (6) ◽  
pp. R47-R79 ◽  
Author(s):  
Boris N Zakhariev ◽  
Vladimir M Chabanov
Keyword(s):  
Inverse Problem ◽  
Quantum Mechanics ◽  
New Situation

scholarly journals TIME-DEPENDENT PARASUPERSYMMETRY IN QUANTUM MECHANICS

1996 ◽  
Vol 11 (26) ◽  
pp. 2095-2104 ◽  
Author(s):  
BORIS F. SAMSONOV
Keyword(s):  
Quantum Mechanics ◽  
Discrete Spectrum ◽  
Schrodinger Equation ◽  
Free Particle ◽  
Time Dependent ◽  
Darboux Transformations ◽  
Integral Of Motion ◽  
One Dimensional ◽  
A Chain ◽  
The One

Parasupersymmetry of the one-dimensional time-dependent Schrödinger equation is established. It is intimately connected with a chain of the time-dependent Darboux transformations. As an example a parasupersymmetric model of nonrelativistic free particle with threefold degenerate discrete spectrum of an integral of motion is constructed.

EXACTLY-SOLVABLE COUPLED-CHANNEL MODELS FROM SUPERSYMMETRIC QUANTUM MECHANICS

2008 ◽  
Vol 22 (23) ◽  
pp. 2277-2286 ◽  
Author(s):  
JEAN-MARC SPARENBERG ◽  
ANDREY M. PUPASOV ◽  
BORIS F. SAMSONOV ◽  
DANIEL BAYE
Keyword(s):  
Inverse Problem ◽  
Quantum Mechanics ◽  
Bound States ◽  
Potential Model ◽  
Analytical Form ◽  
Exactly Solvable Potential ◽  
Exactly Solvable ◽  
Potential Matrix ◽  
Coupled Channel ◽  
Factorization Energy

Starting from a system of N radial Schrödinger equations with a vanishing potential and finite threshold differences between the channels, a coupled N × N exactly-solvable potential model is obtained with the help of a single non-conservative supersymmetric transformation. The obtained potential matrix, which subsumes a result obtained in the literature, has a compact analytical form, as well as its Jost matrix. It depends on N(N + 1)/2 unconstrained parameters and on one upper-bounded parameter, the factorization energy. For N = 2, previous results are reviewed, in particular regarding the number of bound states and resonances of the potential. A schematic inverse problem with one resonance is considered.

SPECTRAL INVERSE PROBLEM IN SUPERSYMMETRIC QUANTUM MECHANICS

1993 ◽  
Vol 08 (23) ◽  
pp. 4123-4129 ◽  
Author(s):  
P.K. BERA ◽  
S. BHATTACHARYYA ◽  
B. TALUKDAR
Keyword(s):  
Inverse Problem ◽  
Quantum Mechanics ◽  
Hydrogen Atom ◽  
State Energy ◽  
Bound State ◽  
Quantization Condition ◽  
Energy Spectra ◽  
Conventional Theory ◽  
Bound State Energy ◽  
Spectral Inverse Problem

The supersymmetric WKB quantization condition is used to study the so-called spectral inverse problem. Wavefunctions for the harmonic oscillator and hydrogen atom are obtained from the knowledge of their bound-state energy spectra. The analysis presented is based essentially on a repackaging of the conventional theory of integral equations.

ON THE GEOMETRY OF QUANTUM MECHANICS

2012 ◽  
Vol 09 (02) ◽  
pp. 1260025
Author(s):  
ELISA ERCOLESSI ◽  
GIUSEPPE MORANDI
Keyword(s):  
Inverse Problem ◽  
Quantum Mechanics ◽  
Berry Phase ◽  
Short Review ◽  
Quantum Inverse ◽  
Alternative Structures ◽  
Physical Problems

We will present a short review of some work we have done in the last ten years with Giuseppe Marmo, on the attempt to formulate some interesting physical problems — such as the Quantum Inverse Problem, Alternative Structures and Berry Phase — in a geometrical setting.

Sign in / Sign up

Export Citation Format

Share Document