Premium
Quantum properties of complete solutions for a new noncentral ring‐shaped potential
Author(s) -
Dong ShiHai,
Chen ChangYuan,
LozadaCassou M.
Publication year - 2005
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.20729
Subject(s) - bound state , diagonal , physics , wave function , quantum mechanics , scattering , scattering amplitude , quantum , annihilation , creation and annihilation operators , amplitude , ring (chemistry) , quantum defect , quantum number , mathematical physics , mathematics , chemistry , geometry , organic chemistry , ion , ionization , rydberg formula
We propose a new exactly solvable ring‐shaped potential V ( r ,θ) = −(α/ r ) + (σ/ r 2 ) + β cos 2 θ/( r 2 sin 2 θ). The exact bound‐state solutions are presented explicitly. The creation and annihilation operators are established directly from the normalized radial wave functions. We present two important recurrence relations among the diagonal matrix elements and obtain some explicit expressions of mean values of r k (8 ≥ k ≥ −11). The exact form of continuum states is also obtained analytically. Comments are made on the calculation formula of phase shifts and the analytical properties of the scattering amplitude. It is interesting to find that the exact form of continuum states will reduce to that of the bound states at the poles of the scattering amplitude. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005