Comparison of numerical methods for the calculation of cold atom collisions
@article{Rawitscher1999ComparisonON, title={Comparison of numerical methods for the calculation of cold atom collisions}, author={George Rawitscher and Brett Daniel Esry and Eite Tiesinga and James P. Burke}, journal={Journal of Chemical Physics}, year={1999}, volume={111}, pages={10418-10426} }
Comparison between three different numerical techniques for solving a coupled channel Schrodinger equation is presented. The benchmark equation, which describes the collision between two ultracold atoms, consists of two channels, each containing the same diagonal Lennard-Jones potential, one of positive and the other of negative energy. The coupling potential is of an exponential form. The methods are (i) a recently developed spectral type integral equation method based on Chebyshev expansions…
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References
SHOWING 1-10 OF 25 REFERENCES
A first-order perturbative numerical method for the solution of the radial schrödinger equation
- Mathematics, Computer Science
- 1976
The finite-element method for energy eigenvalues of quantum mechanical systems
- Physics
- 1989
The finite‐element method provides a convenient and flexible procedure for the calculation of energy eigenvalues of quantum mechanical systems. The levels of accuracy that can be attained in the…
Integral Equation Method for Coupled Schrödinger Equations
- Mathematics
- 1999
A new integral equation method for the numerical solution of the radial Schrodinger equation in one dimension, developed by the authors (1997, J. Comput. Phys.134, 134), is extended to systems of…
Time-dependent quantum-mechanical methods for molecular dynamics
- Physics
- 1988
The basic framework of time-dependent quantum-mechanical methods for molecular dynamics calculations is described. The central problem addressed by computational methods is a discrete representation…
Sum Rules in the Dispersion Theory of Nuclear Reactions
- Mathematics
- 1952
In the first five sections the dispersion theory is developed with an internal region $V$ whose boundary $S$ is quite close to the nuclear surface. Two types of quantities then occur: those like the…
Dispersion coefficients for alkali-metal dimers.
- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1994
Knowledge of the long-range interaction between atoms and molecules is of fundamental importance for low-energy and low-temperature collisions. The electronic interaction between the charge…
Integral Equation Method for the Continuous Spectrum Radial Schrödinger Equation
- Mathematics
- 1997
A new approach to the numerical solution of boundary value problems for differential equations, which originated in recent papers by Greengard and Rokhlin, is improved and adapted to the numerical…
Many‐body effects and resonances in universal quantum sticking of cold atoms to surfaces
- Physics
- 1994
The role of shape resonances and many‐body effects on universal quantum sticking of ultracold atoms onto solid surfaces is examined analytically and computationally using an exactly solvable…
Atomic photoionization in a strong magnetic field
- Physics
- 1983
The photoionization of hydrogen atoms in a strong magnetic field is formulated as a multichannel problem by representing the asymptotic electron wave function in cylindrical coordinates. Departures…