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IssuesArchive of Issues2001-6pp.84-86

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A. A. Lokshin and E. A. Sagomonyan, "Virial theorem for the generalized Hill equation," Mech. Solids. 36 (6), 84-86 (2001)
Year 2001 Volume 36 Number 6 Pages 84-86
Title Virial theorem for the generalized Hill equation
Author(s) A. A. Lokshin (Moscow)
E. A. Sagomonyan (Moscow)
Abstract Hill equation with nonperiodic boundary conditions is known to govern the propagation of harmonic waves in periodic structures [1]. Similar equations of more general form appear also in quantum chemistry [2]. In the present paper, a new integral identity for solutions of these equations is established. This integral identity is related by its nature to the virial theorem.
References
1.  L. Brilluin and M. Parody, Wave Propagation in Periodic Structures [Russian translation], Izd-vo Inostr. Lit-ry, Moscow, 1959.
2.  J. Connor, T. Uzer, and R. Marcus, "Eigenvalues of the Schroedinger equation for a periodic potential with nonperiodic boundary conditions," J. Chem. Phys., Vol. 80, pp. 5095-5105, 1984.
3.  M. Reed and B. Simon, Methods of Modern Mathematical Physics. Volume 4. Operator Analysis [Russian translation], Mir, Moscow, 1982.
Received 05 July 1999
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