Physics – Mathematical Physics
Scientific paper
2008-12-30
Reports on Mathematical Physics, vol. 65, no. 1, 2010, pp. 29-76.
Physics
Mathematical Physics
51 pages
Scientific paper
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".
Kovalchuk Vasyl
Sławianowski Jan Jerzy
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