International Journal of Theoretical Physics

, Volume 52, Issue 6, pp 2038–2045 | Cite as

Crypto-Unitary Forms of Quantum Evolution Operators

Article

Abstract

The description of quantum evolution using unitary operator \(\mathfrak{u}(t)=\exp(-{\rm i}\mathfrak{h}t)\) requires that the underlying self-adjoint quantum Hamiltonian \(\mathfrak{h}\) remains time-independent. In a way extending the so called \(\mathcal{PT}\)-symmetric quantum mechanics to the models with manifestly time-dependent “charge” \(\mathcal{C}(t)\) we propose and describe an extension of such an exponential-operator approach to evolution to the manifestly time-dependent self-adjoint quantum Hamiltonians \(\mathfrak{h}(t)\).

Keywords

PT-symmetric quantum mechanics Time-dependent Schroedinger equation Manifestly time-dependent Hermitian Hamiltonians Manifestly time-dependent Dyson maps Equivalent time-independent non-Hermitian Hamiltonians 

Notes

Acknowledgement

Work supported by GAČR, grant Nr. P203/11/1433.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Nuclear Physics Institute ASCRŘežCzech Republic

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