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Harrell, Evans M.; Klaus, M.

On the double-well problem for Dirac operators. (English) Zbl 0529.35062

Ann. Inst. Henri Poincaré, Sect. A 38, 153-166 (1983).
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Cited in 13 Documents

MSC:

35P20 Asymptotic distributions of eigenvalues in context of PDEs
35Q99 Partial differential equations of mathematical physics and other areas of application
81Q15 Perturbation theories for operators and differential equations in quantum theory
35B20 Perturbations in context of PDEs

Keywords:

double-well problem; Dirac operators; spectroscopy of diatomic molecules; asymptotics of the eigenfunctions

Citations:

Zbl 0445.35036
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Full Text: Numdam EuDML

References:

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[8] E.M. Harrell , Comm. Math. Phys. , t. 75 , 1980 , p. 239 - 261 . Article | MR 581948 | Zbl 0445.35036 · Zbl 0445.35036 · doi:10.1007/BF01212711
[9] T. Kato , Perturbation theory for linear operators , 2 nd ed., New York , Springer , 1976 . MR 407617 | Zbl 0342.47009 · Zbl 0342.47009
[10] M. Reed , B. Simon , Methods of Modern Mathematical Physics, Vol. IV: Analysis of Operators , New York , Academic Press , 1978 . Zbl 0401.47001 · Zbl 0401.47001
[11] This is modeled on an argument made in conversation by R. Seiler.
[12] J.M. Combes , L. Thomas , Comm. Math. Phys. , t. 34 , 1973 , p. 251 - 270 . Article | MR 391792 | Zbl 0271.35062 · Zbl 0271.35062 · doi:10.1007/BF01646473
[13] T. Kato , Comm. Pure and Applied Math. , t. 10 , 1957 , p. 151 - 177 . MR 88318 | Zbl 0077.20904 · Zbl 0077.20904 · doi:10.1002/cpa.3160100201
[14] R. Ahlrichs , Theor. Chim. Acta , t. 41 , 1976 , p. 7 - 15 .
[15] E.M. Harrell , Proc. Am. Math. Soc. , t. 69 , 1978 , p. 271 - 276 . MR 487733 | Zbl 0345.47007 · Zbl 0345.47007 · doi:10.2307/2042610
[16] E.B. Davies , The twisting trick for double-well Hamiltonians , Comm. Math. Physics , to appear. Article | MR 678157 | Zbl 0524.47019 · Zbl 0524.47019 · doi:10.1007/BF01208725
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