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.

中文翻译：

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能级的薛定ding方程为量子态确定的概率分布的线性方程

在本文中，我们表明，具有哈密顿量N × N矩阵H的Qudit系统（自旋j，N级原子）的能谱由N ² × N ²矩阵ℋ的特征值方程及其特征向量确定| p ⟩用部件，这是在量子力学的概率表示与量子态确定概率分布。我们基于状态向量的常规Schrödinger方程导出该方程。ψ。我们将详细讨论量子位的示例，并研究能级的新熵特征。