Schrödinger and related equations as Hamiltonian systems, manifolds of second-order tensors and new ideas of nonlinearity in quantum mechanics

DOI10.1016/S0034-4877(10)00008-XzbMath1200.81056arXiv0812.5055OpenAlexW2154727579MaRDI QIDQ989383

Jan Jerzy Sławianowski, Vasyl Kovalchuk

Publication date: 20 August 2010

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.5055

zbMATH Keywords

conservation lawsHermitian formsSchrödinger equationquantum paradoxesDirac formalismHamiltonian systems on manifolds of scalar productsscalar product as a dynamical variable\(GL(n,\mathbb C) \)-invarianceessential nonperturbative nonlinearityfinite-dimensional Hilbert spacefinite-level quantum systems

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Variational principles of physics (49S05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (2)

Nonlinear quantum-dynamical system based on the Kadomtsev-Petviashvili II equation ⋮ Quantization of systems with internal degrees of freedom in two-dimensional manifolds

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