### 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 |
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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 |
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Country | Brazil |

City | Cuiaba City |

Period | 20.4.09 → 24.4.09 |

### Fingerprint

### ASJC Scopus subject areas

- General

### Cite this

*Proceedings of Science*

**On singular lagrangian underlying the Schrodinger equation.** / Deriglazov, Alexei.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of Science.*5th International School on Field Theory and Gravitation, ISFTG 2009, Cuiaba City, Brazil, 20.4.09.

}

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.

UR - http://www.scopus.com/inward/record.url?scp=84883613014&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883613014&partnerID=8YFLogxK

M3 - Conference contribution

BT - Proceedings of Science

ER -