Analytic solutions of the double ring-shaped Coulomb potential in quantum mechanics

The exact solutions of the Schr6dinger equation with the double ring-shaped Coulomb potential are presented, including the bound states, continuous states on the ＂k/2π scale＂, and the calculation formula of the phase shifts. The polar angular wave functions are expressed by constructing the so-calle...

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Veröffentlicht in:	Chinese physics B 2013-10, Vol.22 (10), p.94-100
1. Verfasser:	陈昌远陆法林孙东升董世海
Format:	Artikel
Sprache:	eng
Schlagworte:	Construction Coulomb potential Exact solutions Mathematical analysis Polynomials Quantum mechanics Schroedinger equation Wave functions 勒让德多项式库仑势束缚态环形精确解解析解连续状态量子力学
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Beschreibung
Zusammenfassung:	The exact solutions of the Schr6dinger equation with the double ring-shaped Coulomb potential are presented, including the bound states, continuous states on the ＂k/2π scale＂, and the calculation formula of the phase shifts. The polar angular wave functions are expressed by constructing the so-called super-universal associated Legendre polynomials. Some special cases are discussed in detail.
ISSN:	1674-1056 2058-3834 1741-4199
DOI:	10.1088/1674-1056/22/10/100302