 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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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 |
| << Previous article | Volume 36, Issue 6 / 2001 | Next article >> |
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