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Volumn 70, Issue 3, 2004, Pages

Uniform approximation of wave functions with improved semiclassical transformation amplitudes and Gram-Schmidt orthogonalization

Author keywords

[No Author keywords available]

Indexed keywords

AMPLITUDE MODULATION; EIGENVALUES AND EIGENFUNCTIONS; FREQUENCIES; HARMONIC ANALYSIS; INTEGRAL EQUATIONS; NUMERICAL ANALYSIS; OSCILLATORS (ELECTRONIC); THEOREM PROVING;

EID: 19644401553     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.70.032101     Document Type: Article
Times cited : (20)

References (29)
  • 5
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    • note
    • m(θ).
  • 8
    • 85015774396 scopus 로고    scopus 로고
    • note
    • m), where K(J) is the classical Hamiltonian function for angle-action variables.
  • 9
    • 85015797935 scopus 로고    scopus 로고
    • note
    • cl(q, θ) exists when π/2 < θ mod 2π< 3π/2. However, the integrands of the integral representations in Eqs. (C.62a,b) of Ref. [6] are periodic with period π. (The definition of the variable θ in Ref. [6] and in the present paper is such that θ=0 when p=0 and q>0.)
  • 10
    • 85015770629 scopus 로고    scopus 로고
    • note
    • cl(q, θ) as the Legendre transform of Hamilton's characteristic function for this potential.
  • 11
    • 85015745162 scopus 로고    scopus 로고
    • note
    • 2/1 - α] for α>0 and script q sign=0, 1. The analytic continuation of this identity to arbitary α(=-z) is invoked in the steps leading to Eq. (9).
  • 14
    • 85015786751 scopus 로고    scopus 로고
    • note
    • s{θ-arcsin[sin θ/cos(πq/a)]}, where arcsin denotes the principal value of the inverse sine function.
  • 15
    • 85015759847 scopus 로고    scopus 로고
    • note
    • 1/2cos θ}.
  • 16
    • 85015780440 scopus 로고    scopus 로고
    • note
    • If Θ is the angle between two wave functions defined using inner products, then cos Θ is of the order of I/Α.
  • 17
    • 0004245694 scopus 로고
    • U.S. GPO, Washington, DC, Chap. 22
    • Ultraspherical or Gegenbauer polynomials are discussed in, for example, Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (U.S. GPO, Washington, DC, 1964), Chap. 22.
    • (1964) Handbook of Mathematical Functions
    • Abramowitz, M.1    Stegun, I.A.2
  • 18
    • 34147138162 scopus 로고
    • G. Pöschl and E. Teller, Z. Phys. 83, 143 (1933); F. Gori and L. de la Torre, Eur. J. Phys. 24, 1 (2003).
    • (1933) Z. Phys. , vol.83 , pp. 143
    • Pöschl, G.1    Teller, E.2
  • 20
    • 8644291268 scopus 로고    scopus 로고
    • M.S. dissertation, Kuwait University
    • J. Al-Modhayan, M.S. dissertation, Kuwait University, 2002.
    • (2002)
    • Al-Modhayan, J.1
  • 21
    • 0004176653 scopus 로고    scopus 로고
    • Addison-Wesley, Reading, MA
    • Approximate normalization is achieved by employing the simple estimate given in Eq. (2.78) in M. Brack and R. K. Bhaduri, Semiclassical Physics (Addison-Wesley, Reading, MA, 1997).
    • (1997) Semiclassical Physics
    • Brack, M.1    Bhaduri, R.K.2
  • 22
    • 85015767711 scopus 로고    scopus 로고
    • note
    • In making this demand, I am implicitly taking advantage of the fact that the semiclassical method under consideration is exact for the simple harmonic oscillator.
  • 23
    • 85015728935 scopus 로고    scopus 로고
    • note
    • cr is guaranteed).
  • 24
    • 85015726725 scopus 로고    scopus 로고
    • note
    • 2)] common to all wave functions of the related harmonic oscillator problem.
  • 25
    • 12144268141 scopus 로고
    • P. M. Morse, Phys. Rev. 34, 57 (1929); L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Pergamon, Oxford, 1965), pp. 72-3.
    • (1929) Phys. Rev. , vol.34 , pp. 57
    • Morse, P.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.