Deformed algebras, position-dependent effective masses and curved spaces: an exactly solvable Coulomb problem. (English) Zbl 1063.81070

The authors first show that 3 current unconvential Schrödinger equations (with deformed canonical commutation relation resp. position-dependent effective mass resp. curved space) are equivalent if their relevant functions (deforming function resp. position-dependent mass resp. diagonal metric) satisfy a simple relation. Then they study a Coulomb problem with standard potential and a deforming function linear in \(r\). They determine spectrum and wavefunctions by using all 3 different interpretations. They get only a finite number of bound states (in correspondence to the old result for the Coulomb potential in a space with constant negative curvature).


81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
81U15 Exactly and quasi-solvable systems arising in quantum theory
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
81Q99 General mathematical topics and methods in quantum theory
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