s . co m p - ph ] 2 7 Se p 20 05 Gradient Symplectic Algorithms for Solving the Radial Schrödinger Equation
نویسنده
چکیده
The radial Schrödinger equation for a spherically symmetric potential can be regarded as a one dimensional classical harmonic oscillator with a time-dependent spring constant. For solving classical dynamics problems, symplectic integrators are well known for their excellent conservation properties. The class of gradient symplectic algorithms is particularly suited for solving harmonic oscillator dynamics. By use of Suzuki’s rule for decomposing time-ordered operators, these algorithms can be easily applied to the Schrödinger equation. We demonstrate the power of this class of gradient algorithms by solving the spectrum of highly singular radial potentials using Killingbeck’s method of backward Newton-Ralphson iterations.
منابع مشابه
Gradient symplectic algorithms for solving the radial Schrodinger equation.
The radial Schrodinger equation for a spherically symmetric potential can be regarded as a one-dimensional classical harmonic oscillator with a time-dependent spring constant. For solving classical dynamics problems, symplectic integrators are well known for their excellent conservation properties. The class of gradient symplectic algorithms is particularly suited for solving harmonic-oscillato...
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