On Oscillation Theorem for Two-Component Schrodinger Equation

V. I. Pupyshev; E. A. Pazyuk; A. V. Stolyarov; M. Tamanis; R. Ferber

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arXiv · 0907.1380

On Oscillation Theorem for Two-Component Schrodinger Equation

V. I. Pupyshev·E. A. Pazyuk·A. V. Stolyarov·M. Tamanis·R. Ferber

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Abstract

Conventional one-dimensional oscillation theorem is found to be violated for multi-component Schrödinger equations in a general case while for two-component eigenstates coupled by the sign-constant potential operator the following statements are valid: (1) the ground state ($v = 0$) is not degenerate; and (2) the arithmetic mean of nodes $n_1$, $n_2$ for the two-component wavefunction never exceeds the ordering number $v$ of eigenstate: $(n_1 + n_2)/2\leq v$.

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V. I. Pupyshev, E. A. Pazyuk, A. V. Stolyarov, M. Tamanis, R. Ferber. 2010-03-10. On Oscillation Theorem for Two-Component Schrodinger Equation. https://arxiv.org/abs/0907.1380

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