scholarly journals The auxiliary field method and approximate analytical solutions of the Schrödinger equation with exponential potentials

2009 ◽  
Vol 42 (24) ◽  
pp. 245301 ◽  
Author(s):  
Bernard Silvestre-Brac ◽  
Claude Semay ◽  
Fabien Buisseret
Keyword(s):  
Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Field Method ◽  
Auxiliary Field ◽  
Approximate Analytical Solutions

scholarly journals SEMIRELATIVISTIC HAMILTONIANS AND THE AUXILIARY FIELD METHOD

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4695-4726 ◽  
Author(s):  
BERNARD SILVESTRE-BRAC ◽  
CLAUDE SEMAY ◽  
FABIEN BUISSERET
Keyword(s):  
Schrödinger Equation ◽  
Power Law ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Field Method ◽  
Auxiliary Field ◽  
Square Root ◽  
Exact Results ◽  
Approximate Analytical Solutions ◽  
Envelope Theory

Approximate analytical closed energy formulas for semirelativistic Hamiltonians of the form [Formula: see text] are obtained within the framework of the auxiliary field method. This method, which is equivalent to the envelope theory, has been recently proposed as a powerful tool to get approximate analytical solutions of the Schrödinger equation. Various shapes for the potential V(r) are investigated: power-law, funnel, square root, and Yukawa. A comparison with the exact results is discussed in detail.

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

scholarly journals Convergent Analysis of Energy Conservative Algorithm for the Nonlinear Schrödinger Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Lv Zhong-Quan ◽  
Gong Yue-Zheng ◽  
Wang Yu-Shun
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Pseudospectral Method ◽  
Field Method ◽  
Nonlinear Schrodinger Equation ◽  
Fourier Pseudospectral Method ◽  
Nonlinear Schrödinger ◽  
Vector Field Method ◽  
Energy Conservation Law

Using average vector field method in time and Fourier pseudospectral method in space, we obtain an energy-preserving scheme for the nonlinear Schrödinger equation. We prove that the proposed method conserves the discrete global energy exactly. A deduction argument is used to prove that the numerical solution is convergent to the exact solution in discreteL2norm. Some numerical results are reported to illustrate the efficiency of the numerical scheme in preserving the energy conservation law.

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

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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