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Revista brasileira de fisica

Supersymmetric quantum mechanics and new potentials

Elso Drigo Filho

Published Jan 1, 1990• 3 citations
OpenAlex

Abstract

Using supersymmetric quantum mechanics we generalize some exactly solvable potentials: the particle in the box, ~oschl-~eller and Rosen- Morse. We evaluate the new potentials and indicate their eigenfunctions and spectra.

Related papers

The Morse oscillator generalised from supersymmetry

Elso Drigo Filho

Using the factorisation method in supersymmetric quantum mechanics the author determines new potentials from the Morse oscillator. This method is applied although the ladder operators are not used.

Journal of Physics A Mathematical and General•Nov 7, 1988•26 citations

Quantum Mechanical Model with Nonlocal Potential

Zhang Dexing, Cai Shao-Hong

In this paper, using supersymmetric (SUSY) quantum mechanics, we discuss exactly solvable Quantum mechanical model with nonlocal potential. And we present a simple nonlocal presentation of exactly solvable local model, so exactly to obtain energy eigenfunctions and eignvalues.

Chinese Physics C•Sep 5, 2002•0 citations

Quantum Mechanical Model with Nonlocal Potential

Zhang De

In this paper, using supersymmetric (SUSY) quantum mechanics, we discuss exactly solvable Quantum mechanical model with nonlocal potential. And we present a simple nonlocal presentation of exactly solvable local model, so exactly to obtain energy eigenfunctions and eignvalues.

Chinese Physics C•Jan 1, 2002•0 citations

Generation of Time-Independent and Time-Dependent Harmonic Oscillator-Like Potentials Using Supersymmetric Quantum Mechanics

Timothy B. Huber

The harmonic oscillator is a quantum mechanical system that represents one of the most basic potentials. In order to understand the behavior of a particle within this system, the time-independent Schrödinger equation was solved; in other words, its eigenfunctions and eigenvalues were found. The first goal of this study was to construct a family of single parameter potentials and corresponding eigenfunctions with a spectrum similar to that of the harmonic oscillator. This task was achieved by means of supersymmetric quantum mechanics, which utilizes an intertwining operator that relates a known Hamiltonian with another whose potential is to be built. Secondly, a generalization of the technique was used to work with the time-dependent Schrödinger equation to construct new potentials and corresponding solutions.

IU Journal of Undergraduate Research•Dec 16, 2018•0 citations

Supersymmetric quantum mechanics with nonlocal potentials

Je-Young Choi, Seok-In Hong

We consider supersymmetric quantum mechanical models with both local and nonlocal potentials. We present a nonlocal deformation of exactly solvable local models. Its energy eigenfunctions and eigenvalues are determined exactly. We observe that both our model Hamiltonian and its supersymmetric partner may have normalizable zero-energy ground states, in contrast to local models with nonperiodic or periodic potentials.

arXiv:quant-ph/9811024•Physical Review A•Aug 1, 1999•8 citations

Supersymmetric Methods in Quantum, Statistical and Solid State Physics

Georg Junker

As with the earlier edition, this book provides an accessible introduction to supersymmetric quantum mechanics and its applications in quantum, statistical and solid state physics. Building on the earlier edition it now encapsulates the substantial developments that have been made in supersymmetric quantum mechanics in recent years including conditionally exactly solvable systems, models of classical field theory and the many new interesting aspects within the area of stochastic dynamics, the Pauli and Dirac Equation, coherent states and non-linear algebras. Aimed at graduate students and scientists this book provides a thorough review on supersymmetric quantum mechanics and now includes problems and solutions.

Institute of Physics eBooks•Jan 1, 2019•39 citations
The harmonic oscillator is a quantum mechanical system that represents one of the most basic potentials. In order to understand the behavior of a particle within this system, the time-independent Schrödinger equation was solved; in other words, its eigenfunctions and eigenvalues were found. The first goal of this study was to construct a family of single parameter potentials and corresponding eigenfunctions with a spectrum similar to that of the harmonic oscillator. This task was achieved by means of supersymmetric quantum mechanics, which utilizes an intertwining operator that relates a known Hamiltonian with another whose potential is to be built. Secondly, a generalization of the technique was used to work with the time-dependent Schrödinger equation to construct new potentials and corresponding solutions.
As with the earlier edition, this book provides an accessible introduction to supersymmetric quantum mechanics and its applications in quantum, statistical and solid state physics. Building on the earlier edition it now encapsulates the substantial developments that have been made in supersymmetric quantum mechanics in recent years including conditionally exactly solvable systems, models of classical field theory and the many new interesting aspects within the area of stochastic dynamics, the Pauli and Dirac Equation, coherent states and non-linear algebras. Aimed at graduate students and scientists this book provides a thorough review on supersymmetric quantum mechanics and now includes problems and solutions.