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Quantized-Energy Equation for N-Level Atom in the Probability Representation of Quantum Mechanics

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Journal of Russian Laser Research Aims and scope

A Correction to this article was published on 05 January 2021

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Abstract

For Hermitian and non-Hermitian Hamiltonian matrices H, we present the Schr¨odinger equation for qudit (spin-j system, N-level atom) with the state vector |ψ〉 in a new form of the linear eigenvalue equation for the matrix ℋ = (H ⊗ 1N) and the probability eigenvector |p〉 identified with quantum states in the probability representation of quantum mechanics. We discuss the possibility to experimentally detect the difference between the system states described by the solutions, corresponding to the Schrödinger equation with Hermitian and non-Hermitian Hamiltonians, by measuring the probabilities of artificial spin-1/2 projections m = ± 1/2, sets of which are identified with qudit states. We show that different symmetries of systems, including 𝒫𝒯 -symmetry and broken 𝒫𝒯 -symmetry, are determined by a set of N complex eigenvalues of the Hamiltonian matrix H.

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Change history

  • 05 January 2021

    In section Acknowledgments, the Russian Science Foundation Grant No. 1871-10091 should read No. 1971-10091.

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Authors and Affiliations

  1. Lebedev Physical Institute, Russian Academy of Sciences, Leninskii Prospect 53, Moscow, 119991, Russia

    Vladimir N. Chernega, Margarita A. Man’ko & Vladimir I. Man’ko

  2. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow Region, 141700, Russia

    Vladimir I. Man’ko

  3. Russian Quantum Center Skolkovo, Moscow, 143025, Russia

    Vladimir I. Man’ko

  4. Department of Physics, Tomsk State University, Lenin Avenue 36, Tomsk, 634050, Russia

    Vladimir I. Man’ko

Authors
  1. Vladimir N. Chernega
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  2. Margarita A. Man’ko
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  3. Vladimir I. Man’ko
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Correspondence to Vladimir N. Chernega.

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Chernega, V.N., Man’ko, M.A. & Man’ko, V.I. Quantized-Energy Equation for N-Level Atom in the Probability Representation of Quantum Mechanics. J Russ Laser Res 41, 576–583 (2020). https://doi.org/10.1007/s10946-020-09912-7

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  • DOI: https://doi.org/10.1007/s10946-020-09912-7

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