scholarly journals A class of exactly solvable Schrödinger equation with moving boundary condition

2008 ◽  
Vol 372 (14) ◽  
pp. 2368-2373 ◽  
Author(s):  
T.K. Jana ◽  
P. Roy
Keyword(s):  
Boundary Condition ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Moving Boundary ◽  
Exactly Solvable ◽  
Moving Boundary Condition

scholarly journals On the position-dependent mass Schrödinger equation for Mie-type potentials

2021 ◽  
Vol 2090 (1) ◽  
pp. 012165
Author(s):  
G Ovando ◽  
J J Peña ◽  
J Morales ◽  
J López-Bonilla
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Operator ◽  
Constant Mass ◽  
Point Canonical Transformation ◽  
Mass Distributions ◽  
Exactly Solvable ◽  
Reference Problem ◽  
Dependent Mass ◽  
Position Dependent Mass

Abstract The exactly solvable Position Dependent Mass Schrödinger Equation (PDMSE) for Mie-type potentials is presented. To that, by means of a point canonical transformation the exactly solvable constant mass Schrödinger equation is transformed into a PDMSE. The mapping between both Schrödinger equations lets obtain the energy spectra and wave functions for the potential under study. This happens for any selection of the O von Roos ambiguity parameters involved in the kinetic energy operator. The exactly solvable multiparameter exponential-type potential for the constant mass Schrödinger equation constitutes the reference problem allowing to solve the PDMSE for Mie potentials and mass functions of the form given by m(x) = skx s-1/(xs + 1))2. Thereby, as a useful application of our proposal, the particular Lennard-Jones potential is presented as an example of Mie potential by considering the mass distribution m(x) = 6kx 5/(x 6 + 1))2. The proposed method is general and can be straightforwardly applied to the solution of the PDMSE for other potential models and/or with different position-dependent mass distributions.

Singular Perturbation Solution for a Two-Phase Stefan Problem in Outward Solidification

2019 ◽  
Author(s):  
Minghan Xu ◽  
Saad Akhtar ◽  
Mahmoud A. Alzoubi ◽  
Agus P. Sasmito
Keyword(s):  
Boundary Condition ◽  
Porous Media ◽  
Analytical Solution ◽  
Singular Perturbation ◽  
Stefan Problem ◽  
Moving Boundary ◽  
Computational Cost ◽  
Perturbation Solution ◽  
Two Phase ◽  
Moving Boundary Condition

Abstract Mathematical modeling of phase change process in porous media can help ensure the efficient design and operation of thermal energy storage and pipe freezing. Numerical methods generally require high computational power to be applicable in practice. Therefore, it is of great interest to develop accurate and reliable analytical frameworks. This study proposes a singular perturbation solution for a two-phase Stefan problem that describes outward solidification in a finite annular space. The problem solves cylindrical heat conduction equations for both solid and liquid phases, with consideration of a moving boundary condition. Perturbation method takes the advantages of small Stefan number as the perturbation parameter, which intrinsically occurs in porous media. Furthermore, a boundary-fixing technique is used to remove nonlinearity in the moving boundary condition. Two different time scales are separately expanded and evaluated to facilitate the construction of a composite asymptotic solution. The analytical solution is verified against a general numerical model using enthalpy method and local volume-averaged thermal properties. The results indicate that the temperature profile of both phases can be well modeled by singular perturbation theory. The analytical solution is found to have similar conclusions to the numerical analysis with much lesser computational cost.

Exactly solvable effective mass Schrödinger equation with coulomb-like potential

2010 ◽  
Vol 110 (15) ◽  
pp. 2880-2885 ◽  
Author(s):  
C. Pacheco-García ◽  
J. García-Ravelo ◽  
J. Morales ◽  
J. J. Peña
Keyword(s):  
Schrödinger Equation ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Effective Mass Schrödinger Equation ◽  
Exactly Solvable
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