Lower bound of minimal time evolution in quantum mechanics

dc.creatorGiri, Pulak Ranjan
dc.date2007-06-25
dc.date2008-01-14
dc.date.accessioned2026-07-07T11:44:45Z
dc.date.available2026-07-07T11:44:45Z
dc.descriptionWe show that the total time of evolution from the initial quantum state to final quantum state and then back to the initial state, i.e., making a round trip along the great circle over S^2, must have a lower bound in quantum mechanics, if the difference between two eigenstates of the 2\times 2 Hamiltonian is kept fixed. Even the non-hermitian quantum mechanics can not reduce it to arbitrarily small value. In fact, we show that whether one uses a hermitian Hamiltonian or a non-hermitian, the required minimal total time of evolution is same. It is argued that in hermitian quantum mechanics the condition for minimal time evolution can be understood as a constraint coming from the orthogonality of the polarization vector \bf P of the evolving quantum state ρ={1/2}(\bf 1+ \bf{P}\cdot\boldsymbolσ) with the vector \boldsymbol{\mathcal O}(Θ) of the 2\times 2 hermitian Hamiltonians H ={1/2}({\mathcal O}_0\boldsymbol{1}+ \boldsymbol{\mathcal O}(Θ)\cdot\boldsymbolσ) and it is shown that the Hamiltonian H can be parameterized by two independent parameters {\mathcal O}_0 and Θ.
dc.description4 pages, no figure, revtex4
dc.identifierhttps://arxiv.org/abs/0706.3653
dc.identifierhttp://arxiv.org/abs/0706.3653
dc.identifierInt.J.Theor.Phys.47:2095-2100,2008
dc.identifierdoi:10.1007/s10773-008-9650-0
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/201663
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.titleLower bound of minimal time evolution in quantum mechanics
dc.typetext

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