On the derivation of the Herman-Kluk propagator

Journal of Physics A: Mathematical and General

Volumn 39, Issue 18, 2006, Pages 5067-5078

  Deshpande, Sarin A ^a   Ezra, Gregory S ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646196606     PISSN: 03054470     EISSN: 13616447     Source Type: Journal    
DOI: 10.1088/0305-4470/39/18/020     Document Type: Article

References (43)

1. VanVleck J H 1928 The correspondence principle in the statistical interpretation of quantum mechanics Proc. Natl Acad. Sci. 14 178-88
2. Berry M V and Mount K E 1972 Semiclassical approximations in wave mechanics Rep. Prog. Phys. 35 315-97
3. Miller W H 1974 Classical-limit quantum mechanics and the theory of molecular collisions Adv. Chem. Phys. 25 69-177
4. Miller W H 1975 The classical S-matrix in molecular collisions Adv. Chem. Phys. 30 77-136
5. Herman M F and Kluk E 1984 A semiclassical justification for the use of non-spreading wavepackets in dynamics calculations Chem. Phys. 91 27-34
6. Herman M F 1994 Dynamics by semiclassical methods Annu. Rev. Phys. Chem. 45 83-111
7. Gutzwiller M C 1990 Chaos in Classical and Quantum Mechanics (New York: Springer)
8. Child M S 1991 Semiclassical Mechanics with Molecular Applications (New York: Oxford University Press)
9. Heller E J 1991 Cellular dynamics: a new semiclassical approach to time-dependent semiclassical dynamics J. Chem. Phys. 94 2723-9
10. Heller E J 1991 Wavepacket dynamics and quantum chaology Chaos and Quantum Physics ed M-J Giannoni, A Voros and J Zinn-Justin (New York: Elsevier) pp 549-663
11. Sepulveda M A and Grossmann F 1996 Time-dependent semiclassical mechanics Adv. Chem. Phys. 96 191-304
12. Tannor D J and Garashchuk S 2000 Semiclassical calculation of chemical reaction dynamics via wavepacket correlation functions Annu. Rev. Phys. Chem. 51 553-600
13. Miller W H 2001 The semiclassical initial value representation: a potentially practical way for adding quantum effects to classical molecular dynamics simulations J. Phys. Chem. A 105 2942-55
14. Baranger M, de Aguiar M A M, Keck F, Korsch H J and Schellhaass B 2001 Semiclassical approximations in phase space with coherent states J. Phys. A: Math. Gen. 34 7227-86
15. Thoss M and Wang H B 2004 Semiclassical description of molecular dynamics based on initial-value representation methods Annu. Rev. Phys. Chem. 55 299-332
16. Kay K G 2005 Semiclassical initial value treatments of atoms and molecules Annu. Rev. Phys. Chem. 56 255-80
17. Schulman L S 1981 Techniques and Applications of Path Integration (New York: Wiley)
18. Miller W H 1970 Classical S-matrix: numerical application to inelastic collisions J. Chem. Phys. 53 3578-87
19. Marcus R A 1972 Theory of semiclassical transition probabilities (S-matrix) for inelastic and reactive collisions-uniformization with elastic collision trajectories J. Chem. Phys. 56 3548-50
20. Miller W H 1991 Semiclassical time evolution without root searches-comment J. Chem. Phys. 95 9428-30
21. Kay K G 1994 Integral expressions for the semiclassical time-dependent propagator J. Chem. Phys. 100 4377-92
22. Kay K G 1994 Numerical study of semiclassical initial value methods for dynamics J. Chem. Phys. 100 4432-46
23. Kay K G 1994 Semiclassical propagation for multidimensional systems by an initial value method J. Chem. Phys. 101 2250-60
24. Shalashilin D V and Child M S 2003 Locally coupled coherent states and Herman-Kluk dynamics J. Chem. Phys. 118 2061-71
25. Shalashilin D V and Child M S 2004 The phase space CCS approach to quantum and semiclassical molecular dynamics for high-dimensional systems Chem. Phys. 304 103-20
26. Noid W G, Ezra G S and Loring R F 2003 Optical response functions with semiclassical dynamics J. Chem. Phys. 119 1003-20
27. Noid W G, Ezra G S and Loring R F 2004 Semiclassical computation of the vibrational echo J. Chem. Phys. 120 1491-9
28. Heller E J 1981 Frozen Gaussians: a very simple semiclassical approximation J. Chem. Phys. 75 2923-31
29. Klauder J R and Skagerstam B 1985 Coherent States: Applications in Physics and Mathematical Physics (Singapore: World Scientific)
30. Littlejohn R G 1986 The semiclassical evolution of wavepackets Phys. Rep. 138 193-291
31. Hu B, Jie Q L, Li B W and Wang S J 2001 General initial value form of the semiclassical propagator Phys. Rev. A 63
32. Jie Q L, Hu B B and Li B W 2005 Modification to the pre-factor of the semiclassical propagator Europhys. Lett. 69 692-8
33. Grossmann F and Xavier A L 1998 From the coherent state path integral to a semiclassical initial value representation of the quantum mechanical propagator Phys. Lett. A 243 243-8
34. Miller W H 2002 An alternative derivation of the Herman-Kluk (coherent state) semiclassical initial value representation of the time-evolution operator Mol. Phys. 100 397-400
35. Miller W H 2002 On the relation between the semiclassical initial value representation and an exact quantum expansion in time-dependent coherent states J. Phys. Chem. B 106 8132-5
36. Alonso M A and Forbes G W 1999 New approach to semiclassical analysis in mechanics J. Math. Phys. 40 1699-718
37. Shalashilin D V and Child M S 2000 Time dependent quantum propagation in phase space J. Chem. Phys. 113 10028-36
38. Shalashilin D V and Child M S 2001 Multidimensional quantum propagation with the help of coupled coherent states J. Chem. Phys. 115 5367-75
39. Heller E J 1975 Time-dependent approach to semiclassical dynamics J. Chem. Phys. 62 1544-55
40. Houle P A 1998 Semiclassical quantization of spin PhD Thesis Cornell University
41. Herman M F and Coker D F 1999 Classical mechanics and the spreading of localized wave packets in condensed phase molecular systems J. Chem. Phys. 111 1801-8
42. Wang H, Manolopoulos D E and Miller W H 2001 Generalized Filinov transformation of the semiclassical initial value representation J. Chem. Phys. 115 6317-26
43. Child M S, Sherratt P and Sturdy Y K 2004 Properties of the Baranger thawed Gaussian propagator J. Phys. Chem. A 108 8860-5