Abstract
In this paper, we show that the energy spectrum of a qudit system (spin-j, N-level atom) with Hamiltonian N×N matrix H is determined by the equation for eigenvalues of the N2×N2 matrix ℋ and its eigenvectors | p⟩ with components, which are probability distributions identified with quantum states in the probability representation of quantum mechanics. We derive this equation based on the conventional Schrödinger equation for the state vector | ψ⟩. We discuss the example of qubit in detail and study new entropic characteristics of the energy levels.
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04 January 2021
In section Acknowledgments, the Russian Science Foundation Grant No. 1871-10091 should read No. 1971-10091.
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Chernega, V.N., Man’ko, M.A. & Man’ko, V.I. Schrödinger Equation for Energy Levels as a Linear Equation for Probability Distributions Identified with Quantum States. J Russ Laser Res 41, 441–450 (2020). https://doi.org/10.1007/s10946-020-09897-3
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DOI: https://doi.org/10.1007/s10946-020-09897-3