Constraints on Airy function zeros from quantum-mechanical sum rules

Journal of Physics A: Mathematical and Theoretical

Volumn 42, Issue 7, 2009, Pages

  Belloni, M ^a   Robinett, R W ^b  

^a DAVIDSON COLLEGE   (United States)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 64549157496     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/42/7/075203     Document Type: Article

References (21)

1. Vallée O and Soares M 2004 Airy Functions and Applications to Physics (New Jersey: World Scientific)
2. Nesvizhevsky V V et al 2002 Quantum states of neutrons in the Earth's gravitational field Nature 415 297-9
3. Nesvizhevsky V V et al 2002 Measurement of quantum states of neutrons in the Earth's gravitational field Phys. Rev. D 67 102002 (9 p)
4. Gea-Banacloche J 1999 A quantum bouncing ball Am. J. Phys. 67 776-82
5. Robinett R W 2004 Quantum wave packet revivals Phys. Rep. 392 1-119
6. Vallée O 2000 Comment on 'A quantum bouncing ball' by Julio Gea-Banacloche Am. J. Phys. 68 672-3
7. Albright J R 1977 Integrals of products of Airy functions J. Phys. A: Math. Gen. 10 485-90
8. Gordon R G 1969 New method for constructing wavefunctions for bound states and scattering J. Chem. Phys. 51 14-25 (appendix B)
9. Goodmanson D M 2000 A recursion relation for matrix elements of the quantum bouncer. Comment on 'A quantum bouncing ball' by Julio Gea-Banacloche Am. J. Phys. 68 866-8
10. Thomas W 1925 ber die Zahl der Dispersionselectronen, die einem starionären Zustande zugeordnet sind (Vorläufige Mitteilung) Naturwissenschaftern 13 627
11. Kuhn W 1925 ber die Gesamtstärke der von einem Zustande ausgehenden Absorptionslinien Z. Phys. 33 408-12
12. Reiche F and Thomas W 1925 ber die Zahl der dispersionselektronen, die einem stationären Zustand zugeordnet sind Z. Phys. 34 510-25
13. Sukumar C V 1990 Green's functions and a hierarchy of sum rules for the eigenvalues of confining potentials Am. J. Phys. 58 561-5
14. Sukumar C V 2006 Sum rules for confining potentials arXiv:quant-ph/ 0611066v1
15. Belloni M and Robinett R W 2008 Quantum mechanical sum rules for two model systems Am. J. Phys. 76 798-806 (arXiv:0802.2217)
16. Abramowitz M and Stegun I A 1965 Handbook of Mathematical Functions (Washington, DC: National Bureau of Standards, US Printing Office) p 450
17. Bohigas O, Lane A M and Martorell J 1979 Sum rules for nuclear collective excitations Phys. Rep. 5 267-316
18. Wang S 1999 Generalization of the Thomas-Reiche-Kuhn and the Bethe sum rules Phys. Rev. A 60 262-66
19. Bethe H and Jackiw R 1968 Intermediate Quantum Mechanics 2nd edn (New York: Benjamin) chapter 11
20. Jackiw R 1967 Quantum mechanical sum rules Phys. Rev. 157 1220-25
21. Bethe H 1930 Zur Theorie des Durchgangs schneller Korpuskularstrahlen durch Materie Ann. Phys. Lpz. 5 325-400 translated as Theory of the passage of fast corpuscular rays through matter in Selected Works of Hans A. Bethe with Commentary (H Bethe World Scientific Series in 20th Century Physics vol 18) (Singapore: World Scientific) pp 77-154 (1997)