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The pseudo Hermitian invariant operator and time-dependent non-Hermitian Hamiltonian exhibiting a \(\operatorname{SU}(1,1)\; \text{and}\; \operatorname{SU}(2)\) dynamical symmetry. (English) Zbl 1394.81122

Summary: We study the time evolution of quantum systems with a time-dependent non-Hermitian Hamiltonian exhibiting a \(\operatorname{SU}(1,1)\; \text{and}\; \operatorname{SU}(2)\) dynamical symmetry. With a time-dependent metric, the pseudo-Hermitian invariant operator is constructed in the same manner as for both the \(\operatorname{SU}(1,1)\; \text{and}\; \operatorname{SU}(2)\) systems. The exact common solutions of the Schrödinger equations for both the \(\operatorname{SU}(1,1)\; \text{and}\; \operatorname{SU}(2)\) systems are obtained in terms of eigenstates of the pseudo-Hermitian invariant operator. Finally some interesting physical applications are suggested and discussed.{
©2018 American Institute of Physics}

MSC:

81Q12 Nonselfadjoint operator theory in quantum theory including creation and destruction operators
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
35Q41 Time-dependent Schrödinger equations and Dirac equations
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