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The structure of semiclassical asymptotic expansions of anitsymmetric solutions of the stationary Schrödinger equation. (English. Russian original) Zbl 1032.81012

Math. Notes 67, No. 2, 207-217 (2000); translation from Mat. Zametki 67, No. 2, 257-269 (2000).
Summary: We consider the semiclassical asymptotics of eigenfunctions for the Hamiltonian of a quantum-mechanical system of \(N\) identical fermions with \(d\) degrees of freedom without spin interaction. In the one-dimensional case \((d= 1)\), examples are known in which the ground antisymmetric state in the semiclassical limit is the product of \(N(N - 1)/2\) two-particle wave functions. We construct a nontrivial generalization of this property for \(d>1\).

MSC:

81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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References:

[1] Maslov, V. P., A new variational principle for fermions, Mat. Zametki, 62, 4, 633-634 (1997) · Zbl 1031.81518
[2] Maslov, V. P., Operational Methods (1973), Moscow: Nauka, Moscow
[3] Maslov, V. P., The Complex WKB Method for Nonlinear Equations (1977), Moscow: Nauka, Moscow · Zbl 0449.58001
[4] Landau, L. D.; Lifshits, E. M., Quantum Mechanics (1963), Moscow: Fizmatlit, Moscow
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[6] A. É. Ruuge, “A variational principle for semiclassical fermions,”Mat. Zametki [Math. Notes] (to appear). · Zbl 1032.81516
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