Solving the two-dimensional Schrödinger equation using basis truncation: A hands-on review and a controversial case

Exact Solutions of position dependent mass Schrodinger equation with Pseudoharmonic Oscillator and its thermal properties using extended Nikiforov-Uvarov method

“…The concepts of Schrödinger equation with position-dependent mass (PDM) has a growing interest to many researchers in physics and related fields due to its applications in condensed matter physics [1][2] and other physical phenomena such as the behaviour of the charge carriers in semiconductor heterostructures [3], He clusters and heterostructures [4], abrupt heterojunctions [5], quantum dots physics [6], quantum wells and polarons [7][8]. Others applications of Schrodinger equation with PDM includes superlattices [9] band structures [10],chemical and molecular physics [11][12] and optoelectronics and high-speed electronics devices in semiconductor physics [13][14].The Schrodinger equation with PDM can be solved using different analytical techniques such as Darboux transformation [15],factorization method [16],Nikiforov-Uvarov method [17],supersymmetry and shape invariance [18][19], point canonical transformation [20] among others. Various potential models, Kratzer potential, Poschl-Teller potential, Morse potential, Coulomb potential, Hulthen potential (see Refs.…”