### 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 = (- frac(ℏ^{2}, 2 m) Δ + V) φ{symbol} + i ℏ ∂_{t} φ{symbol}, where the real field φ{symbol} (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 φ{symbol}. After introduction the field into the formalism, its mathematical structure becomes analogous to those of electrodynamics.

Original language | English |
---|---|

Pages (from-to) | 3920-3923 |

Number of pages | 4 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 373 |

Issue number | 43 |

DOIs | |

Publication status | Published - 19 Oct 2009 |

### Fingerprint

### Keywords

- Constrained theories
- Lagrangian formulation
- Schrödinger equation

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*373*(43), 3920-3923. https://doi.org/10.1016/j.physleta.2009.08.050

**On singular Lagrangian underlying the Schrödinger equation.** / Deriglazov, A. A.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 373, no. 43, pp. 3920-3923. https://doi.org/10.1016/j.physleta.2009.08.050

}

TY - JOUR

T1 - On singular Lagrangian underlying the Schrödinger equation

AU - Deriglazov, A. A.

PY - 2009/10/19

Y1 - 2009/10/19

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 = (- frac(ℏ2, 2 m) Δ + V) φ{symbol} + i ℏ ∂t φ{symbol}, where the real field φ{symbol} (t, xi) is some solution of nonsingular Lagrangian theory being specified below. Preservation of probability turns out to be the energy conservation law for the field φ{symbol}. 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 = (- frac(ℏ2, 2 m) Δ + V) φ{symbol} + i ℏ ∂t φ{symbol}, where the real field φ{symbol} (t, xi) is some solution of nonsingular Lagrangian theory being specified below. Preservation of probability turns out to be the energy conservation law for the field φ{symbol}. After introduction the field into the formalism, its mathematical structure becomes analogous to those of electrodynamics.

KW - Constrained theories

KW - Lagrangian formulation

KW - Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=70349330479&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70349330479&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2009.08.050

DO - 10.1016/j.physleta.2009.08.050

M3 - Article

AN - SCOPUS:70349330479

VL - 373

SP - 3920

EP - 3923

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 43

ER -