Derivation of Schwinger variational principles

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 319, Issue 3-4, 2003, Pages 233-239

  Szmytkowski, Radosław ^a  

^a GDANSK UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Quantum scattering; Schwinger principles; Variational methods

Indexed keywords

LAGRANGE MULTIPLIERS; QUANTUM THEORY;

MATRIX ELEMENTS; QUANTUM MECHANICAL POTENTIAL; QUANTUM SCATTERING; SCHWINGER PRINCIPLES; SCHWINGER VARIATIONAL PRINCIPLE; TRANSITION OPERATORS; VARIATIONAL METHODS;

VARIATIONAL TECHNIQUES;

ARTICLE; ELECTRIC POTENTIAL; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; NEUTRON SCATTERING; QUANTUM MECHANICS;

EID: 0344440963     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2003.10.026     Document Type: Article

References (14)

1. A. Messiah, Quantum Mechanics, Vol. 2, North-Holland, Amsterdam, 1962, pp. 862-863.
2. M.L. Goldberger, K.M. Watson, Collision Theory, Wiley, New York, 1964, pp. 320-322.
3. C.J. Joachain, Quantum Collision Theory, North-Holland, Amsterdam, 1975, pp. 233-238. This book is a noteworthy exception in that although the bilinear principle (5.5) appears in it in the usual mysterious way, it contains a derivation of the fractional principle (5.6) from the principle (5.5) along the lines presented by us in Appendix A.
4. R.G. Newton, Scattering Theory of Waves and Particles, 2nd Edition, Springer, New York, 1982, pp. 318-320.
5. B.H. Bransden, Atomic Collision Theory, 2nd Edition, Benjamin/Cummings, Reading, MA, 1983, pp. 65-66.
6. E. Gerjuoy, A.R.P. Rau, L. Spruch, Rev. Mod. Phys. 55 (1983) 725; There are some omissions in the relevant literature cited in that work, the most important being: G.C. Pomraning, J. Soc. Indust. Appl. Math. 13 (1965) 511; G.C. Pomraning, Nucl. Sci. Eng. 29 (1967) 220; O.H. Crawford, J. Math. Phys. 18 (1977) 1241.
7. E. Gerjuoy, A.R.P. Rau, L. Spruch, Rev. Mod. Phys. 55 (1983) 725; There are some omissions in the relevant literature cited in that work, the most important being: G.C. Pomraning, J. Soc. Indust. Appl. Math. 13 (1965) 511; G.C. Pomraning, Nucl. Sci. Eng. 29 (1967) 220; O.H. Crawford, J. Math. Phys. 18 (1977) 1241.
8. E. Gerjuoy, A.R.P. Rau, L. Spruch, Rev. Mod. Phys. 55 (1983) 725; There are some omissions in the relevant literature cited in that work, the most important being: G.C. Pomraning, J. Soc. Indust. Appl. Math. 13 (1965) 511; G.C. Pomraning, Nucl. Sci. Eng. 29 (1967) 220; O.H. Crawford, J. Math. Phys. 18 (1977) 1241.
9. E. Gerjuoy, A.R.P. Rau, L. Spruch, Rev. Mod. Phys. 55 (1983) 725; There are some omissions in the relevant literature cited in that work, the most important being: G.C. Pomraning, J. Soc. Indust. Appl. Math. 13 (1965) 511; G.C. Pomraning, Nucl. Sci. Eng. 29 (1967) 220; O.H. Crawford, J. Math. Phys. 18 (1977) 1241.
10. R. Szmytkowski, J. Math. Phys. 39 (1998) 5231; R. Szmytkowski, J. Math. Phys. 40 (1999) 4181, Erratum.
11. R. Szmytkowski, J. Math. Phys. 39 (1998) 5231; R. Szmytkowski, J. Math. Phys. 40 (1999) 4181, Erratum.
12. E.W. McDaniel, Atomic Collisions. Electron and Photon Projectiles, Wiley, New York, 1989, p. 156.
13. P.M. Morse, H. Feshbach, Methods of Theoretical Physics, Part II, McGraw-Hill, New York, 1953, pp. 1111-1112.
14. R. Szmytkowski, K. Mielewczyk, unpublished.