| Original Articles |
|
|
|
|
Multisymplectic Geometry and Its Applications for the Schrodinger Equation in Quantum Mechanics |
| CHEN Jing-Bo |
| Institute of Geology and Geophysics, Chinese Academy of Sciences, PO Box 9825, Beijing 100029 |
|
| Cite this article: |
|
CHEN Jing-Bo 2007 Chin. Phys. Lett. 24 370-373 |
|
|
|
|
Abstract Multisymplectic geometry for the Schrödinger equation in quantum mechanics is presented. This formalism of multisymplectic geometry provides a concise and complete introduction to the Schrödinger equation. The Schrödinger equation, its associated energy and momentum evolution equations, and the multisymplectic form are derived directly from the variational principle. Some applications are also explored.
|
| Keywords:
11.10.Ef
03.65.Ca
|
|
|
Received: 28 August 2006
Published: 24 February 2007
|
|
|
|
|
|
|
|
[1] Marsden J E, Patrick G P and Shkoller S 1998 Comm.Math. Phys. 199 351
[2] Chen J B 2002 Lett. Math. Phys. 61 63
[3] Bridges T J 1997 Math. Proc. Cam. Phil. Soc. 121 147
[4] Bridges T J and Reich S 2001 Phys. Lett. A 284 184
[5] Chen J B 2005 Lett. Math. Phys. 71 243
[6] Hong J L, Liu Y, Munthe-Kass H and Zanna A 2002 AMultisymplectic Scheme for Schrödinger Equations with VariableCoefficients (preprint)
[7] Olver P J 1993 Applications of Lie Groups toDifferential Equations 2nd edn (New York: Springer)
[8] Veselov A P 1988 Funct. Anal. Appl. 22 83
[9] Chen J B and Qin M Z 2002 Numer. Meth. Part. Diff. Eq. 18 523
[10] Reich S 2000 J. Comput. Phys. 157 473
[11] Lee T D 1982 Phys. Lett. B 122 217
[12] Kane C, Marsden J E and Ortiz M 1999 J. Math. Phys. 40 3353
[13] Chen J B, Guo H Y and Wu K 2003 J. Math. Phys. 441688 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
