Geometric Phases, Symmetries of Dynamical Invariants, and Exact Solution of the Schrödinger Equation

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dc.creatorMostafazadeh, Ali
dc.date2001-01-02
dc.date2001-07-11
dc.date.accessioned2026-07-07T10:54:58Z
dc.date.available2026-07-07T10:54:58Z
dc.descriptionWe introduce the notion of the geometrically equivalent quantum systems (GEQS) as quantum systems that lead to the same geometric phases for a given complete set of initial state vectors. We give a characterization of the GEQS. These systems have a common dynamical invariant, and their Hamiltonians and evolution operators are related by symmetry transformations of the invariant. If the invariant is $T$-periodic, the corresponding class of GEQS includes a system with a $T$-periodic Hamiltonian. We apply our general results to study the classes of GEQS that include a system with a cranked Hamiltonian $H(t)=e^{-iKt}H_0e^{iKt}$. We show that the cranking operator $K$ also belongs to this class. Hence, in spite of the fact that it is time-independent, it leads to nontrivial cyclic evolutions and geometric phases. Our analysis allows for an explicit construction of a complete set of nonstationary cyclic states of any time-independent simple harmonic oscillator. The period of these cyclic states is half the characteristic period of the oscillator.
dc.descriptionAccepted for publication in J. Phys. A
dc.identifierhttps://arxiv.org/abs/quant-ph/0101010
dc.identifierhttp://arxiv.org/abs/quant-ph/0101010
dc.identifierJ.Phys.A34:6325-6338,2001
dc.identifierdoi:10.1088/0305-4470/34/32/312
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/185974
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleGeometric Phases, Symmetries of Dynamical Invariants, and Exact Solution of the Schrödinger Equation
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