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Volumn 61, Issue 6, 2000, Pages 6392-6398

Semiclassical approximation to the partition function of a particle in D dimensions

Author keywords

[No Author keywords available]

Indexed keywords

ANHARMONIC OSCILLATORS; CENTRAL POTENTIALS; D DIMENSIONS; FIELD THEORY; PARTITION FUNCTIONS; PATH INTEGRAL; SEMI-CLASSICAL APPROXIMATION; TWO-POINT FUNCTION;

EID: 0034206987     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.6392     Document Type: Article
Times cited : (17)

References (27)
  • 7
    • 0003769394 scopus 로고
    • A. Voros, J. Zinn-Justin, North-Holland, Amsterdam
    • M. Berry, in Chaos and Quantum Physics, edited by A. Voros, and J. Zinn-Justin, M.-J. Giannoni (North-Holland, Amsterdam, 1991).
    • (1991) Chaos and Quantum Physics
    • Berry, M.1
  • 8
    • 85036412244 scopus 로고    scopus 로고
    • This is to be contrasted with the semiclassical approximation in quantum mechanics, where one has to find all the stationary points of the action, irrespective of being minima, maxima, or points of inflection
    • This is to be contrasted with the semiclassical approximation in quantum mechanics, where one has to find all the stationary points of the action, irrespective of being minima, maxima, or points of inflection.
  • 10
    • 85036407095 scopus 로고    scopus 로고
    • in Trends in Theoretical Physics II, edited by H. Falomir, R. E. Gamboa Saraví, and F. A. Schaposnik, AIP Conf. Proc. No. 484 (AIP, Woodbury, NY, 1999) (e-printquant-ph/9903028
    • C. A. A. de Carvalho and R. M. Cavalcanti, in Trends in Theoretical Physics II, edited by H. Falomir, R. E. Gamboa Saraví, and F. A. Schaposnik, AIP Conf. Proc. No. 484 (AIP, Woodbury, NY, 1999) (e-print quant-ph/9903028).
    • de Carvalho, C.A.A.1    Cavalcanti, R.M.2
  • 21
    • 0003851731 scopus 로고
    • M. Abramowitz, I. A. Stegun, Dover, New York
    • Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover, New York, 1965).
    • (1965) Handbook of Mathematical Functions
  • 22
    • 85036229038 scopus 로고    scopus 로고
    • This definition only makes sense for (Formula presented). For (Formula presented) one must take (Formula presented)with C chosen in such a way that (Formula presented) and (Formula presented) are continuous at (Formula presented). See Ref. 8 for details
    • This definition only makes sense for (Formula presented). For (Formula presented) one must take (Formula presented)with C chosen in such a way that (Formula presented) and (Formula presented) are continuous at (Formula presented). See Ref. 8 for details.
  • 23
    • 85036273191 scopus 로고    scopus 로고
    • order to compute the derivative in Eq. (40), we have approximated (Formula presented) by a rational function using Thiele’s interpolation formula. See Handbook of Mathematical Functions (Ref. 15), formula 25.2.50
    • In order to compute the derivative in Eq. (40), we have approximated (Formula presented) by a rational function using Thiele’s interpolation formula. See Handbook of Mathematical Functions (Ref. 15), formula 25.2.50.
  • 24
    • 85036298673 scopus 로고    scopus 로고
    • For instance, when (Formula presented), Eq. (42) gives values of (Formula presented) (Formula presented), and (Formula presented) that differ from the exact ones by less than 3%, 1%, and 0.1%, respectively
    • For instance, when (Formula presented), Eq. (42) gives values of (Formula presented) (Formula presented), and (Formula presented) that differ from the exact ones by less than 3%, 1%, and 0.1%, respectively.
  • 26
    • 85036289516 scopus 로고    scopus 로고
    • We conjecture that they are in fact invertible for any (Formula presented), except maybe for a finite number of points
    • We conjecture that they are in fact invertible for any (Formula presented), except maybe for a finite number of points.
  • 27
    • 85036431194 scopus 로고    scopus 로고
    • S. Coleman, in The Whys of Subnuclear Physics, edited by A. Zichichi (Plenum, New York, 1979); reproduced in S. Coleman, Aspects of Symmetry (Cambridge University Press, Cambridge, 1985)
    • S. Coleman, in The Whys of Subnuclear Physics, edited by A. Zichichi (Plenum, New York, 1979); reproduced in S. Coleman, Aspects of Symmetry (Cambridge University Press, Cambridge, 1985).


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.