Abstract
The convergence of the Schwinger–DeWitt expansion in quantum mechanics is investigated for a special class of potentials for which the squared derivative of a potential (e.g., the centrifugal potential, the modified Peschle–Teller potential, or the potential specified by the Weierstrass function) is represented as a polynomial in the powers of the potential itself. It has been established for which representatives of the class the expansion diverges and for which it converges (convergence may take place only at certain discrete values of the charge). For potentials singular at zero, the absence of singularities in the formula for the kernel has been demonstrated. A generalization of potentials with a converging expansion to a multidimensional case is proposed.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
