Lower order eigenvalues of the Schrodinger operator

Bingqing Ma

Abstract


Making use of the method introduced by Brands in [4], we consider lower order eigenvalues of the Schrodinger operator in Euclidean domains. We extend an estimate on eigenvalues obtained by Ashbaugh and Benguria in [3].


Keywords


Membrane eigenvalue; Schrodinger operator; Rayleigh-Ritz inequality

Full Text:

PDF

References


H. J. Sun, Q. M. Cheng and H. C. Yang, Lower order eigenvalues of Dirichlet Laplacian, Manuscripta Math., 125 (2008), 139-156.

L. E. Payne, G. Polya and H. F. Weinberger, On the ratio of consecutive eigenvalues, J. Math. Phys., 35 (1956), 289-298.

M. S. Ashbaugh and R. D. Benguria, More bounds on eigenvalue ratios for Dirichlet Laplacians in n dimensions, SIAM J. Math. Anal., 24 (1993), 1622-1651.

J. J. A. M. Brands, Bounds for the ratios of the first three membrane eigenvalues, Arch. Rational Mech. Anal., 16 (1964), 265-268.

D. G. Chen and Q. M. Cheng, Extrinsic estimates for eigenvalues of the Laplace operator, J. Math. Soc. Japan, 60 (2008), 325-339.

G. Y. Huang, X. X. Li and R. W. Xu, Extrinsic estimates for the eigenvalues of SchrÄodinger operator, Geom. Dedicata, 143 (2009), 89-107.




DOI: http://dx.doi.org/10.26713%2Fcma.v5i2.176

Refbacks

  • There are currently no refbacks.


eISSN 0975-8607; pISSN 0976-5905