An underrated entanglement: Riccati and Schrödinger equations

American Journal of Physics

Volumn 65, Issue 3, 1997, Pages 237-243

  Haley, Stephen B ^a,b  

^a UNIVERSITY OF LAUSANNE   (Switzerland)

^b University of California   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031500925     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18535     Document Type: Article

References (38)

1. Rather than citing original centuries-old references, to which most readers do not have easy access, the reader is referred to such citations and interesting historical comments in the books of G. N. Watson, and E. L. Ince.
2. G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge, U.P., London, 1958).
3. E. L. Ince, Ordinary Differential Equations (Dover, New York, 1956).
4. R. Bellman and G. M. Wing, An Introduction to Invariant Imbedding (Wiley, New York, 1976).
5. W. T. Reid, Riccati Differential Equations (Academic, New York, 1972)
6. S. B. Haley and P. Erdos, "Wave propagation in one-dimensional disordered structures," Phys. Rev. B 45, 8572-8584 (1992).
7. An unlabeled Riccati equation appears in Ref. 27, p. 240, as an intermediate step in the derivation of the WKB approximation. Otherwise, there is no hint of its applicability as used here.
8. A. Bohm, Quantum Mechanics Foundations and Applications (Springer-Verlag, Heidelberg, 1994).
9. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Mécanique Quantique (Hermann, Paris, 1973).
10. A. Das and A. C. Melissinos, Quantum Mechanics a Modern Introduction (Gordon and Breach Science, New York, 1986).
11. A. S. Davydov, Quantum Mechanics (Pergamon, London, 1965).
12. D. K. Ferry, Quantum Mechanics (Institute of Physics, Bristol, 1993).
13. S. Flügge, Practical Quantum Mechanics (Springer-Verlag, Heidelberg, 1970).
14. S. Gasiorowicz, Quantum Physics (Wiley, New York, 1974).
15. K. Gottfried, Quantum Mechanics (Addison-Wesley, New York, 1989).
16. H. Haken, Quantum Field Theory in Solids (North-Holland, Amsterdam, 1983).
17. P. R. Holland, The Quantum Theory of Motion (Cambridge U.P., Cambridge, 1993).
18. L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Pergamon, London, 1977), 3rd ed.
19. R. L. Liboff, Introductory Quantum Mechanics (Addison-Wesley, Reading, MA, 1980).
20. E. Merzbacher, Quantum Physics (Wiley, New York, 1974).
21. A. Messiah, Mécanique Quantique (Dunod, Paris, 1960).
22. D. Park, Introduction to the Quantum Theory (McGraw-Hill, New York, 1964).
23. C. Piron, Mécanique Quantique: Bases et Applications (Presses Polytechniques et Universitaires Romandes, Lausanne, 1990).
24. E. Prugovecki, Quantum Mechanics in Hilbert Space (Academic, New York, 1981).
25. J. J. Sakurai, Modern Quantum Mechanics (Benjamin/Cummings, Menlo Park, 1985).
26. L. I. Schiff, Quantum Mechanics (McGraw-Hill, New York, 1949).
27. R. Shankar, Principles of Quantum Mechanics (Plenum, New York, 1980).
28. V. K. Thankappan, Quantum Mechanics (Wiley, New York, 1993), 2nd ed.
29. W. Weizel, Lehrbuch der Theoretischen Physik (Springer-Verlag, Heidelberg, 1958), Zweiter Band.
30. P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
31. 2, based directly on the Schrödinger equation is given in Ref. 22, p. 376; however, no connection is made to the Riccati equation.
32. F. A. Berezin and M. A. Shubin, The Schrödinger Equation (Kluwer Academic, Dordrecht, 1991).
33. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (National Bureau Standards, Washington DC, 1972).
34. E. Kamke, Differentialgleichungen Lösungsmethoden und Lösungen (Chelsa, New York, 1971).
35. D. ter Haar, Problems in Quantum Mechanics (Pion LTD, London, 1975).
36. W. Montroll, "Quantum theory on a network I.", J. Math Phys. 11, 635-648 (1970).
37. P. M. Morse, J. Fisk, and L. Schiff, "Collision of neutron and proton," Phys. Rev. 50, 748-754 (1936).
38. L. Rosenfeld, Nuclear Forces (Interscience, New York, 1948), p. 67.