The Schrödinger kernel of the twisted Laplacian and cyclic models

DOI10.1007/s00013-010-0206-1zbMath1208.47038OpenAlexW2048246081MaRDI QIDQ616148

Shahla Molahajloo, Man-Wah Wong

Publication date: 7 January 2011

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-010-0206-1

zbMATH Keywords

eigenvaluesmagnetic fieldcosmologyheat kernelquantum Hall effectspinsLandau levelsangular momentum operatorHermite operatortwisted Laplaciancyclic modelsSchrödinger kernelsimple harmonic oscillator

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) General theory of partial differential operators (47F05) Pseudodifferential operators (47G30)

Related Items (3)

Coherent states quantization for generalized Bargmann spaces with formulae for their attached Berezin transforms in terms of the Laplacian on \(\mathbb C^{N }\) ⋮ Weyl transforms and solutions to Schrödinger equations for time-dependent Hermite operators ⋮ Semiclassical limits of the Schrödinger kernels on the \(h\)-Heisenberg group

Cites Work

• Spectral and regularity properties of a pseudo-differential calculus related to Landau quantization
• Hierarchical Weyl transforms and the heat semigroup of the hierarchical twisted Laplacian
• Weyl transforms
• Harmonic analysis on the Heisenberg group
• On the Weyl representation of metaplectic operators
• Weyl transforms, the heat kernel and Green function of a degenerate elliptic operator
• Extended Weyl calculus and application to the phase-space Schrödinger equation
• A Cyclic Model of the Universe
• Classes of Degenerate Elliptic Operators in Gelfand-Shilov Spaces
• Symplectically covariant Schrödinger equation in phase space
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