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… 

Tables from this paper

An accurate spectral method for solving the Schroedinger equation

The solution of the Lippman-Schwinger (L-S) integral equation is equivalent to the the solution of the Schroedinger equation. A new numerical algorithm for solving the L-S equation is described in

An economical method to calculate eigenvalues of the Schrödinger equation

A method is presented which is an extension to negative energies of a spectral integral equation method to solve the Schroedinger equation, developed previously for scattering applications. One

A variational R-matrix finite element procedure for solving ultra-cold collision problems

The proposed FEM implementation presents as advantages the possibility of the development of an efficient matrix inversion algorithm which significantly reduces the computation time to calculate the R matrix and makes it numerically competitive.

A novel method for the solution of the Schrödinger equation in the presence of exchange terms

In the Hartree–Fock approximation the Pauli exclusion principle leads to a Schrodinger equation of an integro-differential form. We describe the extension of a new spectral noniterative method

Calculation of the two-body scattering K-matrix in configuration space by an adaptive spectral method

A spectral integral method (IEM) for solving the two-body, one-variable Lippmann–Schwinger equation for the wavefunction in configuration space is generalized to the case of the two-variable

A Spectral Integral Equation Solution of the Gross-Pitaevskii Equation

The Gross-Pitaevskii equation (GPE), that describes the wave function of a number of coherent Bose particles contained in a trap, contains the cube of the normalized wave function, times a factor

Calculation of the two-body T-matrix in configuration space.

A spectral integral method (IEM) for solving the two-body Schrodinger equation in configura- tion space is generalized to the calculation of the corresponding T −matrix. It is found that the

Elastic scattering of cold caesium and rubidium atoms

For elastic scattering of 133Cs atoms by 85Rb and 87Rb atoms, interacting via the X 1 Σ+ and a 3Σ+ molecular states of RbCs, calculations are presented of the scattering length and the effective

Integral Equation Method for Coupled Schrödinger Equations

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

References

SHOWING 1-10 OF 25 REFERENCES

The finite-element method for energy eigenvalues of quantum mechanical systems

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

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

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

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.

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

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

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

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