Smoothness of Wave Functions in Thermal Equilibrium

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dc.creatorTumulka, Roderich
dc.creatorZanghi, Nino
dc.date2005-09-13
dc.date.accessioned2026-07-07T06:22:38Z
dc.date.available2026-07-07T06:22:38Z
dc.descriptionWe consider the thermal equilibrium distribution at inverse temperature $β$, or canonical ensemble, of the wave function $Ψ$ of a quantum system. Since $L^2$ spaces contain more nondifferentiable than differentiable functions, and since the thermal equilibrium distribution is very spread-out, one might expect that $Ψ$ has probability zero to be differentiable. However, we show that for relevant Hamiltonians the contrary is the case: with probability one, $Ψ$ is infinitely often differentiable and even analytic. We also show that with probability one, $Ψ$ lies in the domain of the Hamiltonian.
dc.description16 pages LaTeX, no figures
dc.identifierhttps://arxiv.org/abs/math-ph/0509028
dc.identifierhttp://arxiv.org/abs/math-ph/0509028
dc.identifierJ. Math. Phys. 46 (2005) 112104
dc.identifierdoi:10.1063/1.2109767
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95968
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.subject82B10; 60G15; 60G17
dc.titleSmoothness of Wave Functions in Thermal Equilibrium
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