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Crypto-Unitary Forms of Quantum Evolution Operators

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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 \(\mathfrak{h}(t)\).

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Acknowledgement

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

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  1. Nuclear Physics Institute ASCR, 250 68, Řež, Czech Republic

    Miloslav Znojil

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  1. Miloslav Znojil
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Correspondence to Miloslav Znojil.

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Znojil, M. Crypto-Unitary Forms of Quantum Evolution Operators. Int J Theor Phys 52, 2038–2045 (2013). https://doi.org/10.1007/s10773-012-1451-9

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  • DOI: https://doi.org/10.1007/s10773-012-1451-9

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