Erratum: A kernel of Gel’fand–Levitan type for the three‐dimensional Schrödinger equation [J. Math. Phys. 21, 83 (1980)]

This paper examines three different recent computational schemes (extended simplest equation (ESE) method, modified Kudryashov (MKud) method, and modified Khater (MKha) method) for obtaining novel solitary wave solutions of cubic–quintic nonlinear Helmholtz (CQ–NLH) model. This model is considered as a general model of the well-known Schrödinger equation where it takes into account the effects of backward scattering that are neglected in the more common nonlinear Schrödinger model. Many distinct wave solutions are explained in the different formulas, such as trigonometric, rational, and hyperbolic formulas. These solutions are described in some precise sketches in two- and three-dimensional. The methods’ performance is explained to demonstrate their effectiveness and power.

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Q-BOR–FDTD method for solving Schrodinger equation for rotationally symmetric nanostructures with hydrogenic impurity

Physica Scripta ◽

10.1088/1402-4896/ac48ac ◽

2022 ◽

Author(s):

Arezoo Firoozi ◽

Ahmad Mohammadi ◽

Reza Khordad ◽

Tahmineh Jalali

Keyword(s):

Schrödinger Equation ◽

Analytical Solutions ◽

Schrodinger Equation ◽

Fdtd Method ◽

Three Dimensional ◽

Test Cases ◽

Body Of Revolution ◽

Hydrogenic Impurity ◽

Rotationally Symmetric ◽

Difference Time

Abstract An efficient method inspired by the traditional body of revolution finite-difference time-domain (BOR-FDTD) method is developed to solve the Schrodinger equation for rotationally symmetric problems. As test cases, spherical, cylindrical, cone-like quantum dots, harmonic oscillator, and spherical quantum dot with hydrogenic impurity are investigated to check the efficiency of the proposed method which we coin as Quantum BOR-FDTD (Q-BOR-FDTD) method. The obtained results are analysed and compared to the 3-D FDTD method, and the analytical solutions. Q-BOR-FDTD method proves to be very accurate and time and memory efficient by reducing a three-dimensional problem to a two-dimensional one, therefore one can employ very fine meshes to get very precise results. Moreover, it can be exploited to solve problems including hydrogenic impurities which is not an easy task in the traditional FDTD calculation due to singularity problem. To demonstrate its accuracy, we consider spherical and cone-like core-shell QD with hydrogenic impurity. Comparison with analytical solutions confirms that Q-BOR–FDTD method is very efficient and accurate for solving Schrodinger equation for problems with hydrogenic impurity

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THE FERMION-FERMION EFFECTIVE ACTION FOR THE THREE-DIMENSIONAL MASSIVE THIRRING MODEL

International Journal of Modern Physics A ◽

10.1142/s0217751x94001230 ◽

1994 ◽

Vol 09 (18) ◽

pp. 3143-3151 ◽

Cited By ~ 2

Author(s):

R.F. RIBEIRO ◽

E.R. BEZERRA DE MELLO

Keyword(s):

Schrödinger Equation ◽

Effective Potential ◽

Effective Action ◽

Schrodinger Equation ◽

Three Dimensional ◽

Bound State ◽

Thirring Model ◽

Coupling Constant ◽

Massive Thirring Model

In this paper a nonrelativistic fermion-fermion effective potential for a three-dimensional massive Thirring model is obtained in a 1/N expansion. We show, by analyzing the Schrödinger equation in the presence of this potential, that the system presents a fermion-fermion bound state for a positive value of the coupling constant g.

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