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(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.
| 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 |
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Keywords
- Constrained theories
- Lagrangian formulation
- Schrödinger equation
ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
On singular Lagrangian underlying the Schrödinger equation. / Deriglazov, A. A.
In: Physics Letters, Section A: General, Atomic and Solid State Physics, Vol. 373, No. 43, 19.10.2009, p. 3920-3923.Research output: Contribution to journal › Article
}
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 -