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Physical Review A
Volumn 38, Issue 4, 1988, Pages 1747-1759
Novel approach to tunneling problems
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Indexed keywords

EID: 0001121658     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.38.1747     Document Type: Article
Times cited : (101)
References (28)
  • 10
    • 84926823247 scopus 로고    scopus 로고
    • A. I. Baz, Ya. B. Zeldovich, and A. M. Perelomov, Scattering Reactions and Decay in Nonrelativistic Quantum Mechanics (Israel Program for Scientific Translations, Jerusalem, 1969).
  • 11
    • 84926801463 scopus 로고    scopus 로고
    • These arguments are not valid if U(r) has an another level E1 close to E0 (|E1- E0| app | curlep0|). Since this level is not subtracted by LAMBDA, the wave functions may increase in the inner region.
  • 16
    • 7044255672 scopus 로고
    • Equation (2.28) resembles a well-known relation between the imaginary part of the energy of an instable state and the probability current J (x): Im (E) = J(x) slash2 int0x Φstar(x prime ) Φ (x prime ) dx prime ~, where J(x) =- Im Φstar(x) d Φ (x)/dx and Φ (x) is a solution of the Schrödinger equation for the complex energy, and x is a coordinate near the tunnel end point. However, in order to apply this relation one has to use some prescriptions [see, ] which are meaningful only in the quasiclassical limit.
    • (1973) Phys. Rev. D , vol.7 , pp. 1620
    • Bender, C.M.1    Wu, T.T.2
  • 17
    • 84926867107 scopus 로고    scopus 로고
    • In fact, χk(r) = χk(R) (eα r - e-ατ )/(eα R - e-α R ) for r <= R, since χk(0) =0. Therefore χksprime(R) = α χk(R) up to the terms of order exp (-2 α R).
  • 20
    • 84926801462 scopus 로고    scopus 로고
    • If the barrier potential V(r), Fig. 7, is not a square well in the interior region, r <= R, but a harmonic-oscillator potential (this case could be a more realistic one), then for calculation of GAMMA one has to replace the wave function φ0(R), Eq. (4.15), by the corresponding harmonic-oscillator wave function.
  • 24
    • 84926867106 scopus 로고    scopus 로고
    • Since the quasiclassical action has a logarithmic singularity at hbar -> 0 the straightforward expansion of the integrand in powers of ħ would give an erroneous second term in Eq. (4.28) [ħ instead of (hbar / 2)(1+2 ln 2)]. The correct answer can be found by replacing V(r prime ) by m ω2(r prime - R0)2/2 for r app r1 and performing an analytical integration in this region.

* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.