Abstract
A complete quantum solution provides all possible knowledge of a system, whereas semiclassical theory provides at best approximate solutions in a limited region. Nevertheless, semiclassical methods based on the work of Martin Gutzwiller can provide stunning physical insights in regimes where quantum solutions are opaque. Furthermore, they can provide a unique bridge between the quantum and classical worlds. We illustrate these ideas with an account of a theoretical and experimental attack on the paradigm problem of the hydrogen atom in strong magnetic and electric fields.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
M. C. Gutzwiller, J. Math. Phys. 12, 343 (1971); Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).
M. L. Zimmerman, M. G. Littman, M. M. Kash, and D. Kleppner, Phys. Rev. A. 20, 225l (1979).
T. F. Gallagher, Rydberg Atoms (Cambridge University Press, 1994).
W. R. S. Garton and F. S. Tomkins, Astrophys. J. 158, 839 (1969).
C. Iu, G. R. Welch. M. M. Kash, D. Kleppner, D. Delande, and J.-C. Gay, Phys. Rev. Lett. 66, 145 (1991).
A. Holle, G. Wiebusch, J. Main, H. Rottke, and K. H. Welge, Phys. Rev. Lett. 61, 161 (1988).
A. Holle, J. Main, G. Wiebusch, H. Ratch, and K. H. Welge, Phys. Rev. Lett. 61, 161 (1988).
T. Hankins, Sir William Rowan Hamilton (Johns Hopkins University Press, 1980).
J. Mehra and H. Rechenberg, The Historical Development of Quantum Theory, Vol. 5, Part 2 (Springer, New York, 1987), p. 420.
A. Messiah, Quantum Mechanics, Vol. 1 (North-Holland, Amsterdam, 1964), Chap. VI. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon, 1965), Chap. VII.
K. W. Ford and J. A. Wheeler, Ann. Phys. (N.Y.) 7, 259, 287 (1959).
R. B. Bernstein, in Molecular Beams, J. Ross, ed., Advances in Chemical Physics, Vol. X (Interscience, 1966).
W. H. Miller, J. Chem. Phys. 53, 1949, 3578 (1970). W. H. Miller and T. F. George, J. Chem. Phys. 56, 5668 (1972). R. A. Marcus, J. Chem. Phys. 54, 3965 (1971). J. N. L. Connor and R. A. Marcus, J. Chem. Phys. 55, 5636 (1971). D. W. Noid and R. A. Marcus, J. Chem. Phys. 62, 2119 (1975).
V. P. Maslov and M. V. Fedoriuk, Semiclassical Approximation in Quantum Mechanics (Reidel, Dordrecht, 1981).
I. C. Percival, J. Phys. 6, L229 (1973); Adv. Chem. Phys. 36, 1 (1977). A. Einstein, Verh. Dtsch. Phys. Ges. 19, 82 (1917).
D. Kleppner, M. G. Littman, and M. L. Zimmerman, Sci. American (May 1981), p. 130.
M. V. Berry and M. Tabor, Proc. Roy. Soc. (London) a349, 101 (1976).
Derivation of Closed-Orbit Theory: M. L. Du and J. B. Delos, Phys. Rev. Lett. 58, 1731 (1987); Phys. Rev. A 38, 1896, 1913 (1988). See also E. G. Bogomolnyi, Sov. Phys. JETP 69, 275 (1989), and D. Wintgen and H. Friedrich, Phys. Rev. A 36, 131 (1987). J. M. Mao, J. Shaw, and J. B. Delos, J. Stat. Phys. 68, 51 (1992).
Recurrence Spectroscopy—Magnetic Fields: J. Main, G. Weibusch, K. Welge, J. Shaw, and J. B. Delos, Phys. Rev. A 49, 847 (1994). Parallel Electric and Magnetic Fields: J. M. Mao, K. A. Rapelje, S. J. Blodgett-Ford, J. B. Delos, A. Konig, and H. Rinneberg, Phys. Rev. A 48, 2117 (1993). Electric Fields: J. Gao, J. B. Delos, and M. Baruch, Phys. Rev. A 46, 1449 (1992). J. Gao and J. B. Delos, Phys. Rev. A 56, 356 (1997). Crossed Electric and Magnetic Fields: C. Neumann, R. Ubert, S. Freund, B. Sheehy, K. H. Welge, M. R. Haggerty, and J. B. Delos, Phys. Rev. Lett. 78, 4705 (1997). A. D. Peters and J. B. Delos, Phys. Rev. A 47, 3036 (1993).
Bifurcation Theory for Closed Orbits: K. R. Meyer, J. B. Delos, and J. M. Mao, in Conservative Systems and Quantum Chaos, L. M. Bates and D. L. Rod, eds., Fields Institute Communications 8, 93 (1996) (Am. Math. Soc.). D. A. Sadovskii and J. B. Delos, Phys. Rev. E 54, 2033 (1996). D. A. Sadovskii, J. A. Shaw, and J. B. Delos, Phys. Rev. Lett. 75, 2120 (1995). J. M. Mao and J. B. Delos, Phys. Rev. A 45, 1746 (1992).
Quantum Manifestations of Bifurcations: T. Bartsch, J. Main, and G. Wunner, Ann. Phys. (San Diego)) 277, 19 (1999). K. Weibert, J. Main, and G. Wunner, Ann. Phys. (San Diego) 268, 172 (1998). J. Main and G. Wunner, Phys. Rev. E 57, 7325 (1998); Phys. Rev. A 55, 1743 (1997). A. D. Peters, C. Jaffe, J. Gao, and J. B. Delos, Phys. Rev. A 56, 345 (1997). A. D. Peters, C. Jaffe, and J. B. Delos, Phys. Rev. A 56, 331 (1997). A. D. Peters, C. Jaffe, and J. B. Delos, Phys. Rev. Lett. 73, 2825 (1994).
Scattering from the Ion Core and Combination Orbits: S. M. Owen, T. S. Monteiro, and P. A. Dando, Phys. Rev. E 62, 6388 (2000). P. A. Dando, T. S. Monteiro, and S. M. Owen, Phys. Rev. Lett. 80, 2797 (1998). J. A. Shaw and F. Robicheaux, Phys. Rev. A 58, 3561 (1998). B. Hupper, J. Main, and G. Wunner, Phys. Rev. Lett. 74, 2650 (1995). P. A. Dando, T. S. Monteiro, D. Delande, and K. T. Taylor, Phys. Rev. A 54, 127 (1996); Phys. Rev. Lett. 74, 1099 (1995). J. Gao and J. B. Delos, Phys. Rev. A 46, 1455 (1992); see also Ref. 26.
Orbits in a Node of a Quantum Wave Function: J. A. Shaw and F. Robicheaux, Phys. Rev. A 60, 1728 (1999). J. Main, Phys. Rev. A 60, 1726 (1999). F. Robicheaux and J. A. Shaw, Phys. Rev. A 58, 1043 (1998). J. A. Shaw, J. B. Delos, M. Courtney, and D. Kleppner, Phys. Rev. A 49, 847 (1994).
Time-Dependent Theory: M. R. Haggerty and J. B. Delos, Phys. Rev. A 61, 53406 (2000); see also Ref. 28.
Harmonic Inversion: J. Main, V. A. Mandelshtam, and H. S. Taylor, Phys. Rev. Lett. 78, 4351 (1997); 79, 825 (1997).
M. Courtney, H. Jiao, N. Spellmeyer, and D. Kleppner, Phys. Rev. Lett. 73, 1340 (1994).
M. N. Wise and D. C. Brock, Stud. Hist. Phil. Mod. Phys. 29, 369 (1998).
M. R. Haggerty, N. Spellmeyer, J. B. Delos, and D. Kleppner, Phys. Rev. Lett. 81, 1592 (1998).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kleppner, D., Delos, J.B. Beyond Quantum Mechanics: Insights from the Work of Martin Gutzwiller. Foundations of Physics 31, 593–612 (2001). https://doi.org/10.1023/A:1017512925106
Issue Date:
DOI: https://doi.org/10.1023/A:1017512925106