The Inverse-Cube Central Force Field in Quantum Mechanics

摘要: The problem of the motion a particle in an inverse-cube central force field is fully treated by quantum mechanics and results compared with classical theory. Taking effective radial potential energy as $\frac{S}{{r}^{2}}$, although solutions for negative $0\ensuremath{\geqq}S\ensuremath{\geqq}\frac{\ensuremath{-}{h}^{2}}{32{\ensuremath{\pi}}^{2}\ensuremath{\mu}}$ satisfy usual boundary conditions, they can not be admitted because Hamiltonian Hermitian these solutions. This corresponds to taking ${(l+\frac{1}{2})}^{2}$ place $l(l+1)$ analogue square angular momentum. If we do this, get complete analogy between mechanically allowed solutions, no quantization. involve Bessel functions both real imaginary orders arguments.