Abstract
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.
| Original language | English |
|---|---|
| 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
| Other | 5th International School on Field Theory and Gravitation, ISFTG 2009 |
|---|---|
| Country | Brazil |
| City | Cuiaba City |
| Period | 20.4.09 → 24.4.09 |
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ASJC Scopus subject areas
- General
Cite this
On singular lagrangian underlying the Schrodinger equation. / Deriglazov, Alexei.
Proceedings of Science. 2009.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
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TY - GEN
T1 - On singular lagrangian underlying the Schrodinger equation
AU - Deriglazov, Alexei
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
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M3 - Conference contribution
BT - Proceedings of Science
ER -