We analyze the properties that manifest hamiltonian nature of the Schrödinger equation and show that it can be considered as originating from singular Lagrangian action (with two second class constraints presented in the Hamiltonian formulation). It is used to show that any solution of the Schrödinger equation with time independent potential can be presented in the form ψ = (-h 2/2mδ V)φ + ih̄eφ tf, where the real field φ(t, x i) is some solution of nonsingular Lagrangian theory being specified below. Preservation of probability turns out to be the energy conservation law for the field f. After introduction the field into the formalism, its mathematical structure becomes analogous to those of electrodynamics.
|Title of host publication||Proceedings of Science|
|Publication status||Published - 2009|
|Event||5th International School on Field Theory and Gravitation, ISFTG 2009 - Cuiaba City, Brazil|
Duration: 20 Apr 2009 → 24 Apr 2009
|Other||5th International School on Field Theory and Gravitation, ISFTG 2009|
|Period||20.4.09 → 24.4.09|
ASJC Scopus subject areas