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Volumn 59, Issue 5, 1999, Pages 5272-5277

Phase space localization and matrix element distributions in systems with mixed classical phase space

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EID: 20144372633     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.59.5272     Document Type: Article
Times cited : (11)

References (34)
  • 31
    • 85037192347 scopus 로고    scopus 로고
    • Due to the (Formula presented) symmetry of Eq. (3), the stable orbit perpendicular to the field is already periodic after half of its full period; consequently, (Formula presented) takes only even values. States with positive (negative) z parity (Formula presented) symmetry with respect to (Formula presented) have even (odd) quantum numbers (Formula presented)
    • Due to the (Formula presented) symmetry of Eq. (3), the stable orbit perpendicular to the field is already periodic after half of its full period; consequently, (Formula presented) takes only even values. States with positive (negative) z parity (Formula presented) symmetry with respect to (Formula presented) have even (odd) quantum numbers (Formula presented).
  • 32
    • 85037208440 scopus 로고    scopus 로고
    • The assignment of quantum numbers may be checked by comparison with the corresponding Gutzwiller eigenvalues (Formula presented) cf. 27
    • The assignment of quantum numbers may be checked by comparison with the corresponding Gutzwiller eigenvalues (Formula presented) cf. 27.
  • 33
    • 85037194890 scopus 로고    scopus 로고
    • the case of the hydrogen atom, (Formula presented) is not simply proportional to (Formula presented) It can be shown that in the present case periods are to be replaced by scaled actions in semiclassical expressions. Hence, we require trajectory segments satisfying (Formula presented). It is still possible to use semiclassical sum rules by appealing to the fact that on average, (Formula presented) are proportional to (Formula presented)
    • In the case of the hydrogen atom, (Formula presented) is not simply proportional to (Formula presented) It can be shown that in the present case periods are to be replaced by scaled actions in semiclassical expressions. Hence, we require trajectory segments satisfying (Formula presented). It is still possible to use semiclassical sum rules by appealing to the fact that on average, (Formula presented) are proportional to (Formula presented)


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.