Abstract
The quantum phase problem is investigated by a synthesis of the evolution operator technique and method of invariants. This approach has been found to be quite effective to disclose interrelationship between geometric phases differing in the nature of evolution and to obtain results for them without invoking the concept of parallel transport in the projective Hilbert space. The usefulness of the method developed is ascertained by studying the geometric phases associated with spinor evolutions in rotating magnetic field.
Similar content being viewed by others
References
Y. Aharonov and J. Anandan, Phys. Rev. Lett. 58 (1987) 1593.
J. Anandan, Phys. Lett. A129 (1988) 201.
V.I. Arnold, Mathematical Methods of Classical Mechanics (Springer-Verlag, New York, 1978) chapter 10.
M.V. Berry, Proc. Roy. Soc. London A392 (1984) 45.
T. Bitter and D. Dubbers, Phys. Rev. Lett. 59 (1987) 251.
A. Bohm, Quantum Mechanics, Foundations and Applications, 3rd ed. (Springer-Verlag, New York, 1993) chapter 22.
A. Bohm, B. Kendrick and M.E. Loewe, Int. J. Quantum Chem. 41 (1992) 53.
J.M. Cerveró and J.D. Lajarreta, J. Phys. A: Math. Gen. 22 (1989) L663.
J.M. Cerveró and J.D. Lajarreta, Phys. Lett. A156 (1991) 201.
C.M. Cheng and P.C.W. Fung, J. Phys. A: Math. Gen. 22 (1989) 3493.
H. Goldstein, Classical Mechanics, 2nd ed. (Narosa Pub. House, New Delhi, 1985) chapter 11.
G. Herzberg and H.C. Longuet-Higgins, Disc. Faraday Soc. 35 (1963) 77.
H.C. Longuet-Higgins, Proc. Roy. Soc. London A344 (1975) 147.
B. Kendrick and R.T. Pack, J. Chem. Phys. 102 (1995) 1994.
H. Kozumi and S. Sugano, J. Chem. Phys. 101 (1994) 4903.
A. Kuppermann and Y.S.M. Wu, Chem. Phys. Lett. 205 (1993) 577.
O. Kwon, C. Ahn and Y. Kim, Phys. Rev. A46 (1992) 5354.
L.D. Landau and E.M. Lifshitz, Mechanics, 3rd ed. (Pergamon Press, New York, 1982) chapter 7.
H.R. Lewis, Jr., and W.B. Riesenfeld, J. Math. Phys. 10 (1969) 1458.
C.A. Mead, Chem. Phys. 49 (1980) 23, 33.
C.A. Mead, Rev. Mod. Phys. 64 (1992) 51.
C. Mead and D. Truhlar, J. Chem. Phys. 70 (1979) 2284.
S.S. Mizrahi, Phys. Lett. A138 (1989) 465.
N. Mukunda and R. Simon, Ann. Phys. 228 (1993) 205.
D. Neuhauser, R.S. Judson, D.J. Kouri, D.E. Adelman, N.E. Shafer, D.A.V. Kliner and R.N. Zare, Science 257 (1992) 519.
G. Ni, S. Chen and Y. Shen, Phys. Lett. A197 (1995) 100.
S. Pancharatnam, Proc. Ind. Acad. Sci. A44 (1956) 247.
D.J. Richardson, A.I. Kilvington, K. Green and S.K. Lamoreaux, Phys. Rev. Lett. 61 (1987) 2030.
J.J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, New York, 1985) chapter 5.
J. Samuel and R. Bhandari, Phys. Rev. Lett. 60 (1988) 2339.
A.N. Seleznyova, Phys. Rev. A51 (1995) 950.
B. Simon, Phys. Rev. Lett. 51 (1983) 2167.
E.C.G. Sudarsan, J. Anandan and T.R. Govindarajan, Phys. Lett. A164 (1992) 133.
A.G. Wagh and V.C. Rakhecha, Phys. Lett. A190 (1992) 71.
Y.S.M. Wu and A. Kuppermann, Chem. Phys. Lett. 201 (1993) 178.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Panja, M., Talukdar, B. Geometric phase from a combined evolution‐operator‐invariant technique. Journal of Mathematical Chemistry 21, 183–192 (1997). https://doi.org/10.1023/A:1019170302545
Issue Date:
DOI: https://doi.org/10.1023/A:1019170302545