Year: 1993
Type: article
Abstract: Levinson's theorem for the Dirac equation is known in the form of a sum of positive and negative energy phase shifts at zero momentum related to the total number of bound states. In this Letter we prove a stronger version of Levinson's theorem valid for positive and negative energy phase shifts separately. The surprising result is that, in general, the phase shifts for each sign of the energy do not give the number of bound states with the same sign of the energy (in units of \ensuremath{\pi}), but instead are related to the number of bound states of a certain Schr\"odinger equation, which coincides with the Dirac equation at zero momentum.
Source: Physical Review Letters
Author: Nathan Poliatzky
Institution: Weizmann Institute of Science
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2019997109