Schrödinger trace invariants for homogeneous perturbations of the harmonic oscillator

DOI10.4171/JST/328zbMath1476.35213arXiv1811.06946OpenAlexW3113805752MaRDI QIDQ2043646

Moritz Doll, Steven Zelditch

Publication date: 3 August 2021

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.06946

zbMATH Keywords

trace formulaharmonic oscillatorisotropic calculusthreshold sub-principal perturbation

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) PDEs in connection with quantum mechanics (35Q40)

Related Items (2)

Berezin Transforms Attached to Landau Levels on the Complex Projective Space P^n(ℂ) ⋮ Spectral asymptotic properties of semiregular non-commutative harmonic oscillators

Cites Work

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• Coherent states and applications in mathematical physics.
• Band asymptotics in two dimensions
• Asymptotics of eigenvalue clusters for the Laplacian plus a potential
• Refined Weyl law for homogeneous perturbations of the harmonic oscillator
• Symplectic classification of quadratic forms, and general Mehler formulas
• Toeplitz operators in \(n\)-dimensions
• Central limit theorem for spectral partial Bergman kernels
• Interface asymptotics of partial Bergman kernels around a critical level
• Positivity, complex FIOs, and Toeplitz operators
• Analysis on Fock Spaces

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