Rigged Hilbert spaces and time asymmetry: The case of the upside-down simple harmonic oscillator

DOI10.1007/BF02768929zbMath0893.47049arXivquant-ph/0006011OpenAlexW2049372332MaRDI QIDQ1381690

Gabriel Puccini, Roberto Diener, Mario A. Castagnino, L. P. Lara

Publication date: 12 May 1998

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0006011

zbMATH Keywords

Wigner functionsrigged Hilbert spacesGamow vectorstime asymmetryupside-down harmonic oscillator

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of operator theory in the physical sciences (47N50) Classical equilibrium statistical mechanics (general) (82B05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70)

Related Items (13)

Quantum damped oscillator. II: Bateman's Hamiltonian vs. 2D parabolic potential barrier ⋮ Quantum mechanics of damped systems. II. Damping and parabolic potential barrier ⋮ Quantum Brownian motion ⋮ The Gamow vectors and the Schwinger effect ⋮ A landscape of time asymmetry ⋮ SHORT RANGE POTENTIAL SCHRÖDINGER SCATTERING ⋮ Spectral properties of the squeeze operator ⋮ Koopman's approach to dissipation ⋮ Supersymmetric quantum mechanics of scattering ⋮ Vortex lattices in quantum mechanics ⋮ Hidden conformal symmetry on the black hole photon sphere ⋮ Entropy burst from parabolic potentials ⋮ Anti- \(\mathcal{PT}\)-symmetric harmonic oscillator and its relation to the inverted harmonic oscillator

Cites Work

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• Generalized spectral decomposition of the \(\beta\)-adic baker's transformation and intrinsic irreversibility
• Wigner's function and tunneling
• Dirac kets, Gamov vectors and Gel'fand triplets. The rigged Hilbert space formulation of quantum mechanics. Lectures in mathematical physics at the University of Texas at Austin, USA. Ed. by A. Bohm and J. D. Dollard
• Spectral decomposition of the Renyi map

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