On Oscillation Theorem for Two-Component Schrodinger Equation

2009

Conventional one-dimensional oscillation theorem is found to be violated for multi-component Schr\"{o}dinger 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: $(n_1 + n_2)/2\leq v$.