More on the quantum propagator of a particle in a linear potential

American Journal of Physics

Volumn 64, Issue 8, 1996, Pages 1036-1041

  Arrighini, Giovanni P ^a   Durante, Nicola L ^b   Guidotti, Carla ^a  

^a UNIVERSITY OF PISA   (Italy)

^b Ist Chim Quantistica ed E   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030511305     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18323     Document Type: Article

References (19)

1. See, for example, A. Messiah, Mécanique Quantique (Dunod, Paris, 1960), Chap. XVII.
2. J. J. Sakurai, Modern Quantum Mechanics (revised ed.) (Addison-Wesley, Reading, MA, 1994), Sec. 2.5.
3. L. A. Beauregard, "Propagators in Nonrelativistic Quantum Mechanics," Am. J. Phys. 34, 324-332 (1966).
4. L. Landau and E. Lifchitz, Mécanique Quantique, Théorie Non Relativiste (Éditions MIR, Moscou, 1974), Sec. 24.
5. L. S. Brown and Y. Zhang, "Path Integrals for the Motion of a Particle in a Linear Potential," Am. J. Phys. 62, 806-808 (1994).
6. P. W. Langhoff, S T. Epstein, and M. Karplus, "Aspects of Time-Dependent Perturbation Theory," Rev. Mod. Phys. 44, 602-644 (1972).
7. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
8. See, for example, Ref. 2. Additional sources are R. Shankar, Principles of Quantum Mechanics (Plenum, New York, 1994), 2nd ed.; A. Galindo and P. Pascual, Quantum Mechanics I (Springer-Verlag, Berlin, 1990), Sec. 3.11.
9. See, for example, Ref. 2. Additional sources are R. Shankar, Principles of Quantum Mechanics (Plenum, New York, 1994), 2nd ed.; A. Galindo and P. Pascual, Quantum Mechanics I (Springer-Verlag, Berlin, 1990), Sec. 3.11.
10. See, for example, Ref. 2.
11. R. M. Wilcox, "Exponential Operators and Parameter Differentiation in Quantum Physics," J. Math. Phys. 8, 962-982 (1967).
12. (a) Reference 1, Chap. XII.8;
13. (b) W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, New York, 1973), p. 137.
14. C. A. Moyer, "On the Green Function for a Particle in a Uniform Electric Field," J. Phys. C 6, 1461-1466 (1973).
15. See, for example, Ref. 4. In addition: (i) F. Constantinescu and E. Magyari, Problems in Quantum Mechanics (Pergamon, Oxford, 1971), p. 54;
16. (ii) T. N. Churchill, "Motion of an Electron Wave Packet in a Uniform Electric Field," Am. J. Phys. 46, 537-542 (1978).
17. B. G. Englert and J. Schwinger, "Statistical Atom: Some Quantum Improvements," Phys. Rev. A 29, 2339-2352 (1984).
18. J. Broeckhove, L. Lathouwers, E. Kesteloot, and P. Van Leuven, "On the Equivalence of Time-Dependent Variational Principles," Chem. Phys. Lett. 149, 547-550 (1988).
19. See, for example, J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics (Benjamin, New York, 1968); Ref. 11(b), Chap. 2.