메뉴 건너뛰기




Volumn 76, Issue 9, 2008, Pages 798-806

Quantum mechanical sum rules for two model systems

Author keywords

[No Author keywords available]

Indexed keywords


EID: 51749123744     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.2908194     Document Type: Article
Times cited : (25)

References (61)
  • 1
    • 34250930798 scopus 로고
    • Bemerkung uber die angenaherte Gultigkeit der klassichen Mechanik innerhalb der Quantunmechanik
    • P. Ehrenfest, "Bemerkung uber die angenaherte Gultigkeit der klassichen Mechanik innerhalb der Quantunmechanik," Z. Phys. 45, 455-457 (1927).
    • (1927) Z. Phys , vol.45 , pp. 455-457
    • Ehrenfest, P.1
  • 2
    • 0002078204 scopus 로고
    • The motion of wave packets through their expectation values and uncertainties
    • D. F. Styer, "The motion of wave packets through their expectation values and uncertainties," Am. J. Phys. 58, 742-744 (1990).
    • (1990) Am. J. Phys , vol.58 , pp. 742-744
    • Styer, D.F.1
  • 3
    • 36849131461 scopus 로고
    • Classical and quantum mechanical hypervirial theorems
    • J. Hirschfelder, "Classical and quantum mechanical hypervirial theorems," J. Chem. Phys. 33, 1462-1466 (1960);
    • (1960) J. Chem. Phys , vol.33 , pp. 1462-1466
    • Hirschfelder, J.1
  • 4
    • 0000751693 scopus 로고
    • Some applications of hypervirial theorems to the calculation of average values
    • J. H. Epstein and S. T. Epstein, "Some applications of hypervirial theorems to the calculation of average values," Am. J. Phys. 30, 266-268 (1961).
    • (1961) Am. J. Phys , vol.30 , pp. 266-268
    • Epstein, J.H.1    Epstein, S.T.2
  • 5
    • 2842606265 scopus 로고
    • Über die Zahl der Dispersionselectronen, die einem starionären Zustande zugeordnet sind (Vorläufige Mitteilung)
    • W. Thomas, "Über die Zahl der Dispersionselectronen, die einem starionären Zustande zugeordnet sind (Vorläufige Mitteilung)," Naturwiss. 13, 627 (1925);
    • (1925) Naturwiss , vol.13 , pp. 627
    • Thomas, W.1
  • 6
    • 0000919954 scopus 로고
    • Über die Gesamtstärke der von einem Zustande ausgehenden Absorptionslinien
    • W. Kuhn, "Über die Gesamtstärke der von einem Zustande ausgehenden Absorptionslinien," Z. Phys. 33, 408-412 (1925);
    • (1925) Z. Phys , vol.33 , pp. 408-412
    • Kuhn, W.1
  • 7
    • 0000544428 scopus 로고
    • Über die Zahl der dispersionselektronen, die einem stationären Zustand zugeordnet sind
    • F. Reiche and W. Thomas, "Über die Zahl der dispersionselektronen, die einem stationären Zustand zugeordnet sind," ibid. 34, 510-525 (1925).
    • (1925) Z. Phys , vol.34 , pp. 510-525
    • Reiche, F.1    Thomas, W.2
  • 9
    • 84976870425 scopus 로고    scopus 로고
    • H. Bethe, Zur Theorie des Durchgangs schneller Korpuskularstrahlen durch Materie, Ann. Phys. 5, 325-400 (1930); translated as Theory of the passage of fast corpuscular rays through matter, in Selected Works of Hans A. Bethe with Commentary (World Scientific, Singapore, 1997), pp. 77-154.
    • H. Bethe, "Zur Theorie des Durchgangs schneller Korpuskularstrahlen durch Materie," Ann. Phys. 5, 325-400 (1930); translated as "Theory of the passage of fast corpuscular rays through matter," in Selected Works of Hans A. Bethe with Commentary (World Scientific, Singapore, 1997), pp. 77-154.
  • 11
    • 0343052251 scopus 로고
    • Sum rules for the rotational structure in the molecular transition spectrum
    • I. Shimamura, "Sum rules for the rotational structure in the molecular transition spectrum," J. Phys. B 15, 93-100 (1982).
    • (1982) J. Phys. B , vol.15 , pp. 93-100
    • Shimamura, I.1
  • 12
    • 0007300482 scopus 로고
    • Correlations in space and time and Born approximation scattering in systems of interacting particles
    • L. Van Hove, "Correlations in space and time and Born approximation scattering in systems of interacting particles," Phys. Rev. 95, 249-262 (1954).
    • (1954) Phys. Rev , vol.95 , pp. 249-262
    • Van Hove, L.1
  • 13
    • 0001520347 scopus 로고
    • Conductivity of superconducting films: A sum rule
    • R. A. Ferrell and R. E. Glover III, "Conductivity of superconducting films: A sum rule," Phys. Rev. 109, 1398-1399 (1958).
    • (1958) Phys. Rev , vol.109 , pp. 1398-1399
    • Ferrell, R.A.1    Glover III, R.E.2
  • 14
    • 84989002976 scopus 로고
    • Determination of the superconducting skin depth from the energy gap and sum rule
    • M. Tinkham and R. A. Ferrell, "Determination of the superconducting skin depth from the energy gap and sum rule," Phys. Rev. Lett. 8, 331-333 (1959).
    • (1959) Phys. Rev. Lett , vol.8 , pp. 331-333
    • Tinkham, M.1    Ferrell, R.A.2
  • 15
    • 0032953058 scopus 로고    scopus 로고
    • c cuprates
    • c cuprates," Science 283, 49-52 (1999).
    • (1999) Science , vol.283 , pp. 49-52
    • Basov, D.N.1
  • 16
    • 36049059516 scopus 로고
    • Isospin sum rules in nuclear physics
    • R. Leonardi and M. Rosa-Clot, "Isospin sum rules in nuclear physics," Phys. Rev. Lett. 23, 874-877 (1969).
    • (1969) Phys. Rev. Lett , vol.23 , pp. 874-877
    • Leonardi, R.1    Rosa-Clot, M.2
  • 17
    • 3342894399 scopus 로고
    • Sum rules for nuclear collective excitations
    • O. Bohigas, A. M. Lane, and J. Martorell, "Sum rules for nuclear collective excitations," Phys. Rep. 5, 267-316 (1979).
    • (1979) Phys. Rep , vol.5 , pp. 267-316
    • Bohigas, O.1    Lane, A.M.2    Martorell, J.3
  • 18
    • 0000990101 scopus 로고
    • Sum rules for electron-nuclear scattering
    • G. Orlandini and M. Traini, "Sum rules for electron-nuclear scattering," Rep. Prog. Phys. 54, 257-338 (1991).
    • (1991) Rep. Prog. Phys , vol.54 , pp. 257-338
    • Orlandini, G.1    Traini, M.2
  • 22
    • 4243916254 scopus 로고
    • Asymptotic sum rules at infinite momentum
    • J. D. Bjorken, "Asymptotic sum rules at infinite momentum," Phys. Rev. 179, 1547-1553 (1969).
    • (1969) Phys. Rev , vol.179 , pp. 1547-1553
    • Bjorken, J.D.1
  • 24
    • 0007788633 scopus 로고
    • Hadron properties from QCD sum rules
    • L. J. Reinders, H. Rubinstein, and S. Yazaki, "Hadron properties from QCD sum rules," Phys. Rep. 127, 1-97 (1985).
    • (1985) Phys. Rep , vol.127 , pp. 1-97
    • Reinders, L.J.1    Rubinstein, H.2    Yazaki, S.3
  • 25
    • 0005602580 scopus 로고
    • b, decay and their contributions to the Bjorken sum rule
    • b, decay and their contributions to the Bjorken sum rule," Phys. Lett. B 254, 215-219 (1991);
    • (1991) Phys. Lett. B , vol.254 , pp. 215-219
    • Isgur, N.1    Wise, M.2    Yousefmir, M.3
  • 26
    • 0001537530 scopus 로고
    • Optical sum rule for form factors of heavy mesons
    • M. B. Voloshin, "Optical sum rule for form factors of heavy mesons," Phys. Rev. D 46, 3062-3592 (1992);
    • (1992) Phys. Rev. D , vol.46 , pp. 3062-3592
    • Voloshin, M.B.1
  • 27
    • 0010809904 scopus 로고
    • Conservation laws and sum rules in the heavy quark limit
    • C-K. Chow, "Conservation laws and sum rules in the heavy quark limit," ibid. 51, 3587-3592 (1995).
    • (1995) Phys. Rev. D , vol.51 , pp. 3587-3592
    • Chow, C.-K.1
  • 29
    • 51749089021 scopus 로고    scopus 로고
    • Citation data from , where it is found, for example, that Ref. 22 has been cited over 3200 times.
    • Citation data from , where it is found, for example, that Ref. 22 has been cited over 3200 times.
  • 30
    • 51749109077 scopus 로고    scopus 로고
    • E. Merzbacher, Quantum Mechanics (John Wiley & Sons, New York, 1961), pp. 445-447; D. S. Saxon, Elementary Quantum Mechanics (Holden-Day, San Francisco, 1968), pp. 225-226;
    • E. Merzbacher, Quantum Mechanics (John Wiley & Sons, New York, 1961), pp. 445-447; D. S. Saxon, Elementary Quantum Mechanics (Holden-Day, San Francisco, 1968), pp. 225-226;
  • 32
    • 51749086635 scopus 로고    scopus 로고
    • John Wiley & Sons, New York, 2nd ed, p
    • S. Gasiorowicz, Quantum Physics (John Wiley & Sons, New York, 1996), 2nd ed., p. 277.
    • (1996) Quantum Physics , pp. 277
    • Gasiorowicz, S.1
  • 33
    • 0031495509 scopus 로고    scopus 로고
    • The Thomas-Reiche-Kuhn sum rule and the rigid rotator
    • E. Hadjimichael, W. Currie, and S. Fallieros, "The Thomas-Reiche-Kuhn sum rule and the rigid rotator," Am. J. Phys. 65, 335-341 (1997);
    • (1997) Am. J. Phys , vol.65 , pp. 335-341
    • Hadjimichael, E.1    Currie, W.2    Fallieros, S.3
  • 34
    • 84861876104 scopus 로고    scopus 로고
    • F. M. Fernandez, The Thomas-Reiche-Kuhn sum rule for the rigid rotator, Int. J. Math. Ed. Sci. Tech. 33, 636-640 (2002).
    • F. M. Fernandez, "The Thomas-Reiche-Kuhn sum rule for the rigid rotator," Int. J. Math. Ed. Sci. Tech. 33, 636-640 (2002).
  • 36
    • 0342876907 scopus 로고
    • Quantum mechanical sum rules
    • R. Jackiw, "Quantum mechanical sum rules," Phys. Rev. 157, 1220-1225 (1967).
    • (1967) Phys. Rev , vol.157 , pp. 1220-1225
    • Jackiw, R.1
  • 37
    • 4243685741 scopus 로고    scopus 로고
    • Generalization of the Thomas-Reiche-Kuhn and the Bethe sum rules
    • S. Wang, "Generalization of the Thomas-Reiche-Kuhn and the Bethe sum rules," Phys. Rev. A 60, 262-266 (1999).
    • (1999) Phys. Rev. A , vol.60 , pp. 262-266
    • Wang, S.1
  • 38
    • 0030537230 scopus 로고    scopus 로고
    • The evolution and revival structure of localized quantum wave packets
    • R. Bluhm, V. A. Kostelecky, and J. A. Porter, "The evolution and revival structure of localized quantum wave packets," Am. J. Phys. 64, 944-953 (1996);
    • (1996) Am. J. Phys , vol.64 , pp. 944-953
    • Bluhm, R.1    Kostelecky, V.A.2    Porter, J.A.3
  • 39
    • 0035585177 scopus 로고    scopus 로고
    • Quantum revivals versus classical periodicity in the infinite square well
    • D. F. Styer, "Quantum revivals versus classical periodicity in the infinite square well," ibid. 69, 56-62 (2001).
    • (2001) Am. J. Phys , vol.69 , pp. 56-62
    • Styer, D.F.1
  • 40
    • 0013132521 scopus 로고
    • The Dalgarno-Lewis summation technique: Some comments and examples
    • H. A. Mavromatis, "The Dalgarno-Lewis summation technique: Some comments and examples," Am. J. Phys. 59, 738-744 (1991).
    • (1991) Am. J. Phys , vol.59 , pp. 738-744
    • Mavromatis, H.A.1
  • 41
    • 0028323979 scopus 로고
    • New summation expressions obtained by combining perturbation theory formalisms
    • H. A. Mavromatis, "New summation expressions obtained by combining perturbation theory formalisms," Int. J. Comput. Math. 50, 119-123 (1993).
    • (1993) Int. J. Comput. Math , vol.50 , pp. 119-123
    • Mavromatis, H.A.1
  • 42
    • 84946454610 scopus 로고
    • Sum rules, as a tool for obtaining mathematical series
    • H. A. Mavromatis, "Sum rules, as a tool for obtaining mathematical series," Int. J. Math. Educ. Sci. Tech. 26, 267-313 (1995).
    • (1995) Int. J. Math. Educ. Sci. Tech , vol.26 , pp. 267-313
    • Mavromatis, H.A.1
  • 43
    • 0002678316 scopus 로고
    • The exact calculation of long range forces between atoms by perturbation theory
    • A. Dalgarno and J. T. Lewis, "The exact calculation of long range forces between atoms by perturbation theory," Proc. R. Soc. London, Ser. A 70, 70-74 (1955).
    • (1955) Proc. R. Soc. London, Ser. A , vol.70 , pp. 70-74
    • Dalgarno, A.1    Lewis, J.T.2
  • 44
    • 0001244693 scopus 로고
    • Quantum mechanics of electrons in crystal lattices
    • R. de L. Kronig and W. G. Penney, "Quantum mechanics of electrons in crystal lattices," Proc. R. Soc. London, Ser. A 130, 499-513 (1931).
    • (1931) Proc. R. Soc. London, Ser. A , vol.130 , pp. 499-513
    • Kronig, R.D.L.1    Penney, W.G.2
  • 46
    • 2342599537 scopus 로고
    • Delta potential function model for electronic energies in molecules
    • A. A. Frost, "Delta potential function model for electronic energies in molecules," J. Chem. Phys. 22, 1613 (1954).
    • (1954) J. Chem. Phys , vol.22 , pp. 1613
    • Frost, A.A.1
  • 47
    • 3343024807 scopus 로고    scopus 로고
    • For a long list of references on the use of δ-function potentials in the pedagogical and research literature, see I. R. Lapidus, Bound states and scattering from the one-dimensional hydrogen atom at a boundary, Am. J. Phys. 51, 1137-1139 1983
    • For a long list of references on the use of δ-function potentials in the pedagogical and research literature, see I. R. Lapidus, "Bound states and scattering from the one-dimensional hydrogen atom at a boundary," Am. J. Phys. 51, 1137-1139 (1983).
  • 48
    • 0039066039 scopus 로고
    • Calculation of a bound state wavefunction using free state wavefunctions only
    • K. R. Brownstein, "Calculation of a bound state wavefunction using free state wavefunctions only," Am. J. Phys. 43, 173-176 (1974);
    • (1974) Am. J. Phys , vol.43 , pp. 173-176
    • Brownstein, K.R.1
  • 49
    • 0007073211 scopus 로고
    • Completeness of the energy eigenstates for a delta function potential
    • W. C. Damert, "Completeness of the energy eigenstates for a delta function potential," ibid. 43, 531-534 (1974);
    • (1974) Am. J. Phys , vol.43 , pp. 531-534
    • Damert, W.C.1
  • 50
    • 0034389004 scopus 로고    scopus 로고
    • Completeness of the energy eigenfunctions for the one-dimensional δ-function potential
    • S. H. Patil, "Completeness of the energy eigenfunctions for the one-dimensional δ-function potential," ibid. 68, 712-714 (2000).
    • (2000) Am. J. Phys , vol.68 , pp. 712-714
    • Patil, S.H.1
  • 51
    • 84892305778 scopus 로고
    • Contribution of the continuum in perturbation theory
    • D. Kiang, "Contribution of the continuum in perturbation theory," Am. J. Phys. 45, 308-309 (1977).
    • (1977) Am. J. Phys , vol.45 , pp. 308-309
    • Kiang, D.1
  • 52
    • 0242323994 scopus 로고
    • Higher orders of perturbation theory and summation of series in quantum mechanics and field theory
    • V. S. Popov, V. L. Eletskii, and A. V. Turbiner, "Higher orders of perturbation theory and summation of series in quantum mechanics and field theory," Sov. Phys. JETP 47, 232-242 (1978).
    • (1978) Sov. Phys. JETP , vol.47 , pp. 232-242
    • Popov, V.S.1    Eletskii, V.L.2    Turbiner, A.V.3
  • 53
    • 0345811456 scopus 로고    scopus 로고
    • F. M. Fernandez and E. A Castro, Stark effect in a one-dimensional model atom, Am. J. Phys. 53, 757-760 (1985).
    • F. M. Fernandez and E. A Castro, "Stark effect in a one-dimensional model atom," Am. J. Phys. 53, 757-760 (1985).
  • 54
    • 21844526592 scopus 로고
    • Electric polarizability and the solution of an inhomogeneous differential equation
    • M. A. Maize and C. A. Burkholder, "Electric polarizability and the solution of an inhomogeneous differential equation," Am. J. Phys. 63, 244-247 (1995).
    • (1995) Am. J. Phys , vol.63 , pp. 244-247
    • Maize, M.A.1    Burkholder, C.A.2
  • 56
    • 0004016061 scopus 로고
    • 2nd. ed, John Wiley & Sons, New York
    • E. Merzbacher, Quantum Mechanics, 2nd. ed. (John Wiley & Sons, New York, 1970), pp. 420-425;
    • (1970) Quantum Mechanics , pp. 420-425
    • Merzbacher, E.1
  • 58
    • 0346891612 scopus 로고
    • Continuum wave functions in the calculation of sums involving off-diagonal matrix elements
    • A. R. Ruffa, "Continuum wave functions in the calculation of sums involving off-diagonal matrix elements," Am. J. Phys. 41, 234-241 (1973).
    • (1973) Am. J. Phys , vol.41 , pp. 234-241
    • Ruffa, A.R.1
  • 59
    • 51749103751 scopus 로고    scopus 로고
    • I. S. Gradhsteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, corrected and enlarged edition prepared by A. Jeffrey (Academic Press, New York, 1980), p. 36.
    • I. S. Gradhsteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, corrected and enlarged edition prepared by A. Jeffrey (Academic Press, New York, 1980), p. 36.
  • 60
    • 51749119462 scopus 로고
    • For example, see, 2nd ed, Benjamin, Menlo Park, CA, It is noted there that such sums can be evaluated using the Mittag-Lefler theorem of complex variable theory. This name is often associated with sums of this type
    • For example, see J. Mathews and R. L. Walker, Mathematical Methods of Physics, 2nd ed. (Benjamin, Menlo Park, CA, 1970), pp. 50-55. It is noted there that such sums can be evaluated using the Mittag-Lefler theorem of complex variable theory. This name is often associated with sums of this type.
    • (1970) Mathematical Methods of Physics , pp. 50-55
    • Mathews, J.1    Walker, R.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.