Analytical solutions of a three dimensional time-dependent Schrodinger equation using the Bloch NMR approach for NMR studies

2014 ◽  
Vol 8 ◽  
pp. 2753-2762 ◽  
Author(s):  
Moses E. Emetere
Keyword(s):  
Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Three Dimensional ◽  
Time Dependent ◽  
Nmr Studies

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

Sign in / Sign up

Export Citation Format

Share Document