Year: 1998
Type: article
Abstract: Levinson's theorem for the Schr\"odinger equation with a cylindrically symmetric potential in two dimensions is reestablished by the Sturm-Liouville theorem. The critical case, where the Schr\"odinger equation has a finite zero-energy solution, is analyzed in detail. It is shown that, in comparison to Levinson's theorem in the noncritical case, the half bound state for the $P$ wave, in which the wave function for the zero-energy solution does not decay fast enough at infinity to be square integrable, will cause the phase shift of the $P$ wave at zero energy to increase an additional $\ensuremath{\pi}$.
Source: Physical Review A
Authors: Shi-Hai Dong, Xi-Wen Hou, Zhong-Qi Ma
Institution: Institute of High Energy Physics
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2379422182