Geodesic
Two-sided estimates for eigenvalues of the Schrödinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 3, pp. 412-418 Cet article a éte moissonné depuis la source Math-Net.Ru

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Schrödinger equation is substituted into two systems of $n$ linear equations with $n$ unknown quantitys. The coefficients of these equations are the matrix elements of the hamiltonian between quasiclassical wavefunctions. The solution of these systems give the two-side estimates for eigenvalues of the Schrodinger equation. The relative distance between boundary $\simeq\lambda^k$, where $\lambda$ is the parameter of the quasiclassical decomposition for the $n$-th wavefunction, $k$ is the number of terms in this decomposition. 
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     author = {G. V. Ryazanov},
     title = {Two-sided estimates for eigenvalues of the {Schr\"odinger} equation},
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     pages = {412--418},
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}
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G. V. Ryazanov. Two-sided estimates for eigenvalues of the Schrödinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 3, pp. 412-418. http://geodesic.mathdoc.fr/item/TMF_1975_24_3_a12/

[1] S. Guld, Variatsionnye metody v zadachakh o sobstvennykh znacheniyakh, «Mir», 1970 | MR

[2] S. B. Keller, J. Math. Phys., 2 (1961), 262 ; I. G. Gay, Phys. Rev., 135A (1964), 1220 ; I. D. Donnelly, SIAM J. Number. Anal., 7 (1970), 458 ; I. M. Delves, J. Phys., 5A:8 (1972), 1123 ; M. Cohen, T. Feldmann, J. Phys., 7A:5 (1974), 563 | DOI | MR | Zbl | DOI | MR | DOI | MR | Zbl | MR | MR

[3] Dzh. Polia, G. Sege, Izoperimetricheskie neravenstva v matematicheskoi fizike, IL, 1962 | MR

[4] S. G. Mikhlin, Variatsionnye metody v matematicheskoi fizike, Gostekhizdat, 1957 | MR

[5] L. D. Landau, E. M. Lifshits, Kvantovaya mekhanika, § 51, «Nauka», 1963 | MR