Algebraic Approach to the Position-Dependent Mass Schrödinger Equation for a Singular Oscillator

Abstract

We construct a singular oscillator Hamiltonian with a position-dependent effective mass. We find that an su(1, 1) algebra is the hidden symmetry of this quantum system and the isospectral potentials V(x) depend on the different choices of the m(x). The complete solutions are also presented by using this Lie algebra.

Bound state of solution of Dirac-Coulomb problem with spatially dependent mass

“…The solution of the relativistic Dirac equation for quantum mechanical systems in cases of both spatially dependent mass and constant mass plays an important role in many branches of physics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The Dirac equation with position dependent masshas attracted greater interest as its importance has been recognised [5][6][7][8][9][10][11][12][13][14][15].…”

Solution of the Dirac Equation With Position-Dependent Mass in a Coulomb and Scalar Fields in a Conical Spacetime

“…Quantum mechanical systems with position-dependent mass have attracted a lot of attention and some investigations have been done along this line. [19][20][21][22][23][24][25][26][27][28][29][30] Certainly, these investigations have been done due to the possibility of applications in different scenarios, as for example, in the physics of semiconductors, 31 quantum liquids, 32 many-body problems 33 and in many others physical systems. [34][35][36] The solution of the Dirac equation for a charged particle with positiondependent mass in the Coulomb field was obtained recently.…”

Isospectral potentials for the Schrödinger equation with a position‐dependent mass: Free‐particle potential model

“…Consequently, the exactly solvable SEPDM has attracted considerable attention as demonstrated by already published methods on the subject such as the kinetic energy operator [5], Lie algebras [6,7], supersymmetry [8], and path integration [9] approaches. On the other hand, the Darboux transform (DT) [10] is a very convenient way for constructing new solutions of integrable equations by an algorithm purely algebraic.…”