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arXiv:hep-th/9212116 · WORLD SCIENTIFIC eBooks

COHERENT STATES AND SQUEEZED STATES, SUPERCOHERENT STATES AND SUPERSQUEEZED STATES

Michael Martin Nieto

Published Apr 1, 1994• 4 citations
arXivHTMLPDF

Abstract

This article reports on a program to obtain and understand coherent states for general systems. Most recently this has included supersymmetric systems. A byproduct of this work has been studies of squeezed and supersqueezed states. To obtain a physical understanding of these systems has always been a primary goal. In particular, in the work on supersymmetry an attempt to understand the role of Grassmann numbers in quantum mechanics has been initiated.

DOI
10.1142/9789814327060_0016

Related papers

GENERALIZED SQUEEZED STATES FROM GENERALIZED COHERENT STATES

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Both the coherent states and also the squeezed states of the harmonic oscillator have long been understood from the three classical points of view: the 1) displacement operator, 2) annihilation- (or ladder-) operator, and minimum-uncertainty methods. For general systems, there is the same understanding except for ladder-operator and displacement-operator squeezed states. After reviewing the known concepts, I propose a method for obtaining generalized minimum-uncertainty squeezed states, give examples, and relate it to known concepts. I comment on the remaining concept, that of general displacement-operator squeezed states.

arXiv:hep-th/9311039•May 1, 1994•1 citation

Supersqueezed states from squeezed states

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Supercoherent states as the result of acting of displacement operator on a supersymmetric hamiltonian are introduced and discussed. Berry's phase is calculated for coherent states as their parameters are taken to be varying adiabatically.

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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
This article reports on a program to obtain and understand coherent states for general systems. Most recently this has included supersymmetric systems. A byproduct of this work has been studies of squeezed and supersqueezed states. To obtain a physical understanding of these systems has always been a primary goal. In particular, in the work on supersymmetry an attempt to understand the role of Grassmann numbers in quantum mechanics has been initiated.
Both the coherent states and also the squeezed states of the harmonic oscillator have long been understood from the three classical points of view: the 1) displacement operator, 2) annihilation- (or ladder-) operator, and minimum-uncertainty methods. For general systems, there is the same understanding except for ladder-operator and displacement-operator squeezed states. After reviewing the known concepts, I propose a method for obtaining generalized minimum-uncertainty squeezed states, give examples, and relate it to known concepts. I comment on the remaining concept, that of general displacement-operator squeezed states.
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.