Time-dependent Schrödinger equations having isomorphic symmetry algebras. II. Symmetry algebras, coherent and squeezed states

DOI10.1063/1.533269zbMath0987.81023arXivquant-ph/9811076OpenAlexW3101867563MaRDI QIDQ2737965

Michael Martin Nieto, D. Rodney Truax

Publication date: 30 August 2001

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/9811076

zbMATH Keywords

coherent statessqueezed statestime-varying massquadratic Hamiltoniansnumber-operator statestime-dependent oscillators

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Quantum optics (81V80) Coherent states (81R30)

Related Items (6)

SCHRÖDINGER EQUATIONS WITH TIME-DEPENDENT P² AND X² TERMS ⋮ Time-dependent Schrödinger equations having isomorphic symmetry algebras. I. Classes of interrelated equations ⋮ Note on coherent states and adiabatic connections, curvatures ⋮ The Schrödinger system \(H=-\frac 1 2 e^{\Upsilon(t-t_0)}\partial_{xx}+\frac 1 2\omega^2 e^{-\Upsilon(t-t_0)}x^2\) ⋮ The Schrödinger system \(H=-\frac 1 2(\frac {t_0}{t})^a\partial_{xx}+\frac 1 2\omega^2(\frac{t}{t_0})^bx^2\) ⋮ Form-preserving transformations for Hamiltonians with linear terms in the momentum

Cites Work

• Coherent states for arbitrary Lie group
• Time-dependent Schrödinger equations having isomorphic symmetry algebras. I. Classes of interrelated equations
• Displacement-operator squeezed states. I. Time-dependent systems having isomorphic symmetry algebras
• Displacement-operator squeezed states. II. Examples of time-dependent systems having isomorphic symmetry algebras
• Symmetry of time-dependent Schrödinger equations. I. A classification of time-dependent potentials by their maximal kinematical algebras
• Symmetry of time-dependent Schrödinger equations. II. Exact solutions for the equation {∂x x+2i∂t−2g2(t)x2−2g1(t)x −2g0(t)}Ψ(x, t) = 0
• Squeezed states for general systems
• Coherent and Incoherent States of the Radiation Field

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