Solutions of Helmholtz and Schrödinger Equations with Side Condition and Nonregular Separation of Variables
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Solutions of Helmholtz and Schrödinger Equations with Side Condition and Nonregular Separation of Variables
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| Creator |
Broadbridge, P.
Chanu, C.M. Miller Jr., Willard |
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| Description |
Olver and Rosenau studied group-invariant solutions of (generally nonlinear) partial differential equations through the imposition of a side condition. We apply a similar idea to the special case of finite-dimensional Hamiltonian systems, namely Hamilton-Jacobi, Helmholtz and time-independent Schrödinger equations with potential on N-dimensional Riemannian and pseudo-Riemannian manifolds, but with a linear side condition, where more structure is available. We show that the requirement of N−1 commuting second-order symmetry operators, modulo a second-order linear side condition corresponds to nonregular separation of variables in an orthogonal coordinate system, characterized by a generalized Stäckel matrix. The coordinates and solutions obtainable through true nonregular separation are distinct from those arising through regular separation of variables. We develop the theory for these systems and provide examples.
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| Date |
2019-02-18T17:33:50Z
2019-02-18T17:33:50Z 2012 |
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| Type |
Article
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| Identifier |
Solutions of Helmholtz and Schrödinger Equations with Side Condition and Nonregular Separation of Variables / P. Broadbridge, C.M. Chanu, Willard Miller Jr. // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 36 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 35Q40; 35J05 DOI: http://dx.doi.org/10.3842/SIGMA.2012.089 http://dspace.nbuv.gov.ua/handle/123456789/148652 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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