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Springer eBooks

Introduction (in Honor of Marcos Moshinsky)

Eugene Paul Wigner

Published Jan 1, 2001• 0 citations
Publisher
DOI
10.1007/978-3-662-07791-7_6

Related papers

1. Introduction

Springer eBooks•Nov 22, 2005•0 citations

The harmonic oscillator and the position dependent mass Schrodinger equation: isospectral partners and factorization operators

J. Morales, Gerardo Ovando, José Juan Peña +4 more

One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis à vis the standard Schrödinger equation with constant mass [1].However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position.Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potential as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners.To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schrödinger-like standard equation is applied to the PDMSE.In that case, the former potential associated to the PDMSE and the potential involved in the Schrödinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD) m(x).Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.

AIP conference proceedings•Jan 1, 2010•0 citations

1 Introduction

Stefan Teufel

Lecture notes in mathematics•Jan 1, 2003•0 citations

Group theory and the harmonic oscillator: The work of Marcos Moshinsky

J. Flores, A. Frank, T. H. Seligman

AIP conference proceedings•Jan 1, 1992•0 citations

Correlations between interacting Rydberg atoms

Asaf Paris-Mandoki, Christoph Braun, Sebastian Hofferberth

This paper is a short introduction to Rydberg physics and quantum nonlinear optics using Rydberg atoms. It has been prepared as a compliment to a series of lectures delivered during the Latin American School of Physics “Marcos Moshinsky” 2017. We provide a short introduction to the properties of individual Rydberg atoms and discuss in detail how the interaction potential between Rydberg atom pairs is calculated. We then discuss how this interaction gives rise to the Rydberg blockade mechanism. With the aid of hallmark experiments in the field applications of the blockade for creating correlated quantum systems are discussed. Our aim is to give an overview of this exciting and rapidly evolving field. The interested reader is referred to original work and more comprehensive reviews and tutorials for further details on these subjects.

AIP conference proceedings•Jan 1, 2018•2 citations

Introduction and Theoretical Background

Robert Fickler

Springer theses•Sep 8, 2015•1 citation
One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis à vis the standard Schrödinger equation with constant mass [1].However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position.Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potential as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners.To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schrödinger-like standard equation is applied to the PDMSE.In that case, the former potential associated to the PDMSE and the potential involved in the Schrödinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD) m(x).Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.
This paper is a short introduction to Rydberg physics and quantum nonlinear optics using Rydberg atoms. It has been prepared as a compliment to a series of lectures delivered during the Latin American School of Physics “Marcos Moshinsky” 2017. We provide a short introduction to the properties of individual Rydberg atoms and discuss in detail how the interaction potential between Rydberg atom pairs is calculated. We then discuss how this interaction gives rise to the Rydberg blockade mechanism. With the aid of hallmark experiments in the field applications of the blockade for creating correlated quantum systems are discussed. Our aim is to give an overview of this exciting and rapidly evolving field. The interested reader is referred to original work and more comprehensive reviews and tutorials for further details on these subjects.