A continuum basis of airy functions

作者: Paul M. Hunt

DOI: 10.1080/00268978100102701

关键词:

摘要: Matrix elements between vibrational continuum states are difficult to manipulate because the matrix continuously indexed and typically divergent. Use of Airy wavefunction basis is shown yield tractable xn consisting Dirac delta function its derivatives. Such an may be suitable for use in collision-induced dissociation studies. The used solve time-dependent Schrodinger equation forced harmonic oscillator; agreement with analytical transition probabilities good. This simple system reveals aspects which influence numerical accuracy. Means transforming from oscillator or piecewise-analytic representations also discussed.

参考文章(31)
Aron Kuppermann, George C. Schatz, M. Baer, Quantum mechanical reactive scattering for planar atom plus diatom systems. I. Theory Journal of Chemical Physics. ,vol. 65, pp. 4596- 4623 ,(1976) , 10.1063/1.432916
R. B. Walker, J. C. Light, A. Altenberger‐Siczek, Chemical reaction theory for asymmetric atom–molecule collisions The Journal of Chemical Physics. ,vol. 64, pp. 1166- 1181 ,(1976) , 10.1063/1.432306
M. V. Berry, N. L. Balazs, Nonspreading wave packets American Journal of Physics. ,vol. 47, pp. 264- 267 ,(1979) , 10.1119/1.11855
R. P. Feynman, Space-Time Approach to Non-Relativistic Quantum Mechanics Reviews of Modern Physics. ,vol. 20, pp. 367- 387 ,(1948) , 10.1103/REVMODPHYS.20.367
Don Secrest, B. Robert Johnson, Exact Quantum‐Mechanical Calculation of a Collinear Collision of a Particle with a Harmonic Oscillator The Journal of Chemical Physics. ,vol. 45, pp. 4556- 4570 ,(1966) , 10.1063/1.1727537
William H. Miller, Classical S Matrix: Numerical Application to Inelastic Collisions The Journal of Chemical Physics. ,vol. 53, pp. 3578- 3587 ,(1970) , 10.1063/1.1674535
Gregor Wentzel, Eine Verallgemeinerung der Quantenbedingungen f�r die Zwecke der Wellenmechanik Zeitschrift f�r Physik. ,vol. 38, pp. 518- 529 ,(1926) , 10.1007/BF01397171
Isak Rusinek, R. E. Roberts, Semiclassical calculation for collision induced dissociation Journal of Chemical Physics. ,vol. 65, pp. 872- 880 ,(1976) , 10.1063/1.433155
George Wolken, Quantum mechanical studies of collision induced dissociation: discretization theory Journal of Chemical Physics. ,vol. 63, pp. 528- 533 ,(1975) , 10.1063/1.431082
J R Albright, Integrals of products of Airy functions Journal of Physics A: Mathematical and General. ,vol. 10, pp. 485- 490 ,(1977) , 10.1088/0305-4470/10/4/011