scholarly journals Solutions for Time-Dependent Schrödinger Equations with Applications to Quantum Dots

10.5772/33658 ◽  
2012 ◽  
Author(s):  
Ricardo J.
Keyword(s):  
Quantum Dots ◽  
Time Dependent ◽  
Schrodinger Equations ◽  
Schrödinger Equations

Higher order exponential split operator method for solving time-dependent Schrödinger equations

1992 ◽  
Vol 70 (2) ◽  
pp. 555-559 ◽  
Author(s):  
André D. Bandrauk ◽  
Hai Shen
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Operator Method ◽  
Computation Time ◽  
Time Dependent ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Exponential Form ◽  
Operator Solution ◽  
Split Operator

A new method of splitting exponential operators is proposed for the exponential form of the operator solution to the time-dependent Schrödinger equation. The method is shown to hold for any desired accuracy in the time increment. A comparison of different algorithms is made as a function of accuracy and computation time. Keywords: splitting operator, Fast Fourier Transform (FFT), Schrödinger equations.

SPIN DYNAMICS OF MOLECULAR MAGNET INTERACTING WITH INJECTED ELECTRONS

2003 ◽  
Vol 17 (07) ◽  
pp. 1117-1125 ◽  
Author(s):  
DONG-SHENG HU ◽  
SHI-JIE XIONG
Keyword(s):  
Exchange Interaction ◽  
Time Evolution ◽  
Electron Spin ◽  
Spin Dynamics ◽  
Molecular Magnets ◽  
Time Dependent ◽  
Molecular Magnet ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Local Spin

We investigate the time evolution of the local spin in a molecular magnet interacting with injected electrons. By solving the time-dependent Schrödinger equations, we find that the variation in the magnetization of the molecular magnet and the electron spin crucially depends on the strength of the exchange interaction. We calculate the time evolution of the entanglement between the injected electron and the molecular magnet. It is found that the entanglement oscillates in time and the oscillations are closely related to the changes in the spins. The study provides an estimation of the feasibility of the encoding and read-out by using the polarization of the molecular magnets and the injected electrons.

NUMERICAL SOLUTIONS OF QUANTUM MECHANICAL PROBLEMS USING THE BASIS-SPLINE COLLOCATION METHOD

2001 ◽  
Vol 12 (07) ◽  
pp. 1093-1108 ◽  
Author(s):  
D. O. ODERO ◽  
J. L. PEACHER ◽  
D. H. MADISON
Keyword(s):  
Collocation Method ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Spline Collocation ◽  
Spline Collocation Method

The time-dependent and time-independent Schrödinger equations have been numerically solved for several quantum mechanical problems with known analytical solutions using the basis-spline collocation algorithm. This algorithm has been demonstrated to be efficient and versatile. The results from these calculations illustrate the necessary numerical considerations required for solving both time-independent and time-dependent Schrödinger equations and form a basis that could be used for solving these and similar problems.

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