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The Journal of Chemical Physics
Volumn 100, Issue 3, 1994, Pages 2394-2397
Solving Schrödinger's equation around a desired energy: Application to silicon quantum dots
Author keywords

[No Author keywords available]
Indexed keywords

EID: 0001604458     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.466486     Document Type: Article
Times cited : (480)
References (32)
  • 9
    • 0003462314 scopus 로고
    • One can attempt the “inverse iteration” method (Ref. 9) or inverse iteration combined with Lanczos method
    • Birkhauser, Bostonto calculate energy eigenstates within an energy window. However, the key is to find a fast and efficient way to solve the large dimension linear equations in the inverse iteration method. To our knowledge this has not been accomplished
    • (1985) Lanczos Algorithms for Large Symmetric Eigenvalue Computations
    • Cullum, J.K.1    Willoughby, R.A.2
  • 11
    • 85034920017 scopus 로고    scopus 로고
    • The minimization of F of Eq. (3) is analogous to the minimization of [formula omitted] in the conventional conjugate gradient method (Ref. 6)
    • There are [formula omitted] outside-loop iterations. Inside each iteration, there are [formula omitted] steps of conjugate gradient line minimizations, followed by a subspace diagonalization of [formula omitted] based on the few wave functions [formula omitted] computed simultaneously (four wave functions are calculated here). The [formula omitted] we used [formula omitted] is the square of the typical [formula omitted] value used in conventional conjugate gradient methods based on Ĥ (Ref. 6). The [formula omitted] we used is 5, the same as the typical values used in the conventional methods
  • 16
    • 84950536696 scopus 로고    scopus 로고
    • Standard empirical potentials (Ref. 11) give [formula omitted] only on discrete bulk reciprocal lattice vector G
    • Calculations on finite objects requires a continuous [formula omitted] for all reciprocal vector g. Our fit gives: [formula omitted] [formula omitted] when [formula omitted] and [formula omitted] when [formula omitted] The g and the potentials are in atomic units
  • 32
    • 85034915867 scopus 로고    scopus 로고
    • In Our example of the quantum box shown in Fig. 3
    • we have [formula omitted] eV (measured from the top of bulk valence band) and [formula omitted] for [formula omitted] respectively. Using all three bands gives [formula omitted] eV compared with the exact result [formula omitted] while using only [formula omitted] gives [formula omitted]

* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.