A study of the bound states for square potential wells with position-dependent mass

Abstract

A square potential well with position-dependent mass is studied for bound states. Applying appropriate matching conditions, a transcendental equation is derived for the energy eigenvalues. Numerical results are presented graphically and the variation of the energy of the bound states are calculated as a function of the well-width and mass.

A General type of Liénard Second Order Differential Equation: Classical and Quantum Mechanical Study

“…(12) . Further, we find an extensive study on the position dependence of mass pertaining to various aspects have been carried out by several authors (von Roos, 1983;Quesne and Tkachuk, 2004;Koç and Tütüncüler, 2003;Dutra et al, 2003;Bagchi et al, 2006;Ganguly et al, 2006;Ganguly and Nieto, 2007;Lévai and Özer, 2010;Killingbeck, 2011;Mazharimousavi, 2012;Yahiaoui and Bentaiba, 2012;Mustafa, 2015;Rajbongshi and Singh, 2015). In the present case, we study the discrete nature of spectra and its stability for the newly generated Hamiltonian (Eqn.…”

Double quantum well triple barrier structures: analytical and numerical results

“…4 it is shown the transmissivity of the DQW-TB for a particle's mass of 0.067m e , calculated by using (14)- (16) (14)- (16). Furthermore, for the set of parameters' values used, the central barrier causes the presence of a narrow high transmission peak (T = 0.9646 at 0.1529eV) that does not exist in the transmissivity of the SQW-DB nanostructure.…”

“…Substituting the operator p = -iħd/dx in (24), the Schrödinger equation is rewritten as [16]  Furthermore, the modes  49 ,  50 and  51 represent the particle confined in the barrier regions. As Fig.…”

A new effective mass Hamiltonian and associated Lamé equation: bound states

“…It then ¶ The case of discontinuity in both V (x) and m(x) (e.g. potential-mass step [19] or a quantum well with mass mismatch) corresponds to discontinuity of ψ(x) [51].…”