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On the Methods of One‐Dimensional Auxiliary Problems and of Domain Partitioning: Their Application to Lower Bounds for the Eigenvalues of Schrodinger's Equation

1964; Wiley; Volume: 43; Issue: 1-4 Linguagem: Inglês

10.1002/sapm196443115

0097-1421

Joseph Hersch,

Advanced Mathematical Modeling in Engineering

Journal of Mathematics and PhysicsVolume 43, Issue 1-4 p. 15-26 Article On the Methods of One-Dimensional Auxiliary Problems and of Domain Partitioning: Their Application to Lower Bounds for the Eigenvalues of Schrodinger's Equation† Joseph Hersch, Joseph Hersch Swiss Federal Institute of Technology (E.T.H.) ZürichSearch for more papers by this author Joseph Hersch, Joseph Hersch Swiss Federal Institute of Technology (E.T.H.) ZürichSearch for more papers by this author First published: April 1964 https://doi.org/10.1002/sapm196443115Citations: 9 †This research was essentially performed at the Battelle Memorial Institute in Geneva, Switzerland, and supported by the Battelle Foundation in Columbus, Ohio. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat References 1N. W. Bazley. Lower bounds for eigenvalues with application to the Helium atom. Phys. Rev. 120, 1960, pp. 144–149. 2N. W. Bazley and D. W. Fox. Lower bounds for eigenvalues of Schrödinger's equation. Phys. Rev. 124, 1961, pp. 483–492. 3T. Boggio. Sull'equazione del moto vibratorio delle membrane elastiche. Atti Accad. Lincei, ser. 5, 16 (2° sem), 1907, pp. 386–393. 4G. Fichera and M. Picone. Calcolo per difetto del più basso autovalore di un operatore ellittico del secondo ordine. Rend. Accad. Lincei, ser. 8, 30, 1961, pp. 411–418. 5S. Flügge and H. Marschall. Rechenmethoden der Quantentheorie ( 1. Teil: Elementare Quantenmechanik). Springer, 1952. 6S. H. Gould. Variational methods for eigenvalue problems Univ. of Toronto Press, 1957. 7J. Hersch. Une interprétation du principe de Thomson et son analogue pour la fréquence fondamentale d'une membrane. Application. C. R. Acad. Sci. Paris, 248, 1959, p. 2060. 8J. Hersch. Un principe de maximum pour la fréquence fondamentale déune membrane. C. R. Acad. Sci. Paris, 249, 1959, p. 1074. 9J. Hersch. Sur quelques principes extrémaux de la Physique mathématique. L'Enseignement math., 2e série, 5, 1959, pp. 249–257. 10J. Hersch. Sur la fréquence fondamentale déune membrane vibrante: évaluations par défaut et principe de maximum. Z.A.M.P., 11, 1960, pp. 387–413. 11J. Hersch. Le principe de Thomson comme corollaire de celui de Dirichlet. L'Enseignement math., 2e série, 6, 1960, p. 152. 12J. Hersch. Physical interpretation and strengthening of M. H. Protter's method for vibrating nonhomogeneous membranes; its analogue for Schrödinger's equation. Pacific J. Math. 11, 1961, pp. 971–980. 13J. Hersch. Evaluation par défaut de toutes les fréquences propres d'une membrane à l'aide de “coupures chargees”. C. R. Acad. Sci. Paris, 255, 1962, p. 1286. 14W. W. Hooker. Lower bounds for the first eigenvalue of elliptic equations of orders two and four Dissertation, Tech. Report No. 10, AFOSR, Univ. of California, Berkeley, 1960. 15L. E. Payne and H. F. Weinberger. Lower bounds for vibration frequencies of elastically supported membranes and plates. J. Soc. Indust. Appl. Math., 5, 1957, pp. 171–182. 16E. Picard. Traité d'Analyse, vol. II (1st ed.. 1893), pp. 25–26. 17M. Picone. Criteri sufficienti per il minimo assoluto di un integrale bidimensionale del second'ordine& Atti Accad. Sci. Torino, 95, 1961, pp. 1–11. 18G. Pólya and G. Szegö. Isoperimetric inequalities in mathematical Physics. Princeton University Press, 1951. 19M. H. Protter. Lower bounds for the first eigenvalue of elliptic equations and related topics. Tech. Report No 8, AFOSR, Univ. of California, Berkeley, 1958. 20M. H. Protter. Vibration of a nonhomogeneous membrane. Pacific J. Math., 9, 1959, pp. 1249–55. 21M. H. Protter. Lower bounds for the first eigenvalue of elliptic equations. Annals of Math. 71, 1960, pp. 423–444. 22H. F. Weinberger. A theory of lower bounds for eigenvalues. Tech. Note BN-183, AFOSR, University of Maryland, 1959. Citing Literature Volume43, Issue1-4April 1964Pages 15-26 ReferencesRelatedInformation