Algebraic calculation of the Green’s function for the Hartmann potential

Abstract

Using the so(2,1) Lie algebra and the Baker–Campbell–Hausdorff formulas, the Green’s function for the Hartmann potential is constructed and its bound state energy spectrum is found. Also, this Green’s function is constructed in a coherent state basis and the equivalence of the two descriptions is shown.

Path Integral Discussion for Smorodinsky-Winternitz Potentials: I. Two- and Three Dimensional Euclidean Space

“…Calogero [9], Carpio-Bernido et al [10,11,13,12], Chetouani at al. [17], Gerry [46], Granovsky et al [50], Grosche [56], Guha and Mukherjee [62], Hartmann [63], Kibler et al [76]- [79], [81], Lutsenko et al [90], Vaidya and Boschi-Filho [125], and Zhedanov [131]; compare also the connection with a Coulomb plus Aharonov-Bohm solenoid, e.g. Chetouani et al [18], Kibler and Negadi [80], and Sökmen [117]).…”

Three methods for calculating the Feynman propagator

“…7,18,19 It can also be used to calculate propagators for a wide range of problems. 6,22,23,24,25,26 A coherent-state version of the algebraic method for different problems has been discussed also. 23,27 Because the use of these mathematical tools can be a bit cumbersome at first reading, we prefer to explore a simpler version of this method, which is close to that in Ref.…”

Novel bound states treatment of the two dimensional Schrödinger equation with pseudocentral potentials plus multiparameter noncentral potential

“…Recently, much considerable effort for variety forms of NCPs has been expanded on the solutions of Schrödinger, Dirac and Klein-Gordon equations. The Feynman's path integral treatment [26][27][28][29][30] and the Green's function technique [31,32], the (Lie) algebraic/group theoretical approach [33][34][35][36], nonbijective canonical transformation [3,37], supersymmetric (SUSY) quantum mechanical formalism [38][39][40][41][42][43][44][45][46] and the NU-analytic method [47][48][49][50][51][52][53][54][55][56][57][58] as well as the applications for both relativistic [59][60][61][62][63][64][65][66][67][68][69][70][71] and other nonrelativistic…”