Schr\'odinger and related equations as Hamiltonian systems, manifolds of second-order tensors and new ideas of nonlinearity in quantum mechanics
| Autor: | Sławianowski, J. J., Kovalchuk, V. |
|---|---|
| Rok vydání: | 2008 |
| Předmět: | |
| Zdroj: | Reports on Mathematical Physics, vol. 65, no. 1, 2010, pp. 29-76. |
| Druh dokumentu: | Working Paper |
| Popis: | Considered is the Schr\"odinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting example of "mechanics" with singular Lagrangians, effectively treatable within the framework of Dirac formalism. We discuss also some modified "Schr\"odinger" equations involving second-order time derivatives and introduce a kind of non-direct, non-perturbative, geometrically-motivated nonlinearity based on making the scalar product a dynamical quantity. There are some reasons to expect that this might be a new way of describing open dynamical systems and explaining some quantum "paradoxes". Comment: 51 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|