Notes on the Riccati Equation

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Title:Notes on the Riccati Equation
Creators:
Kryachko, Eugene S.
Journal or Publication Title:
Collection of Czechoslovak Chemical Communications, 70, 7, pp. 941-950
Uncontrolled Keywords:Schrödinger equation, Riccati transformation, Differential equations, Quantum chemistry

Abstract

The relationship between the Riccati and Schrödinger equations is discussed. It is shown that the transformation converting the Riccati equation into its normal form is expressed in terms of the roots of its algebraic part treated as a second-order polynomial. Together with the well-known Riccati transformation, a new transformation which also links the Riccati equation to the second-order linear differential equation is introduced. The latter is actually the Riccati transformation applied to an "inverse" Riccati equation. Two specific forms of the Riccati equation admitting the explicit particular rational solutions are obtained. <p>

Title:Notes on the Riccati Equation
Creators:
Kryachko, Eugene S.
Uncontrolled Keywords:Schrödinger equation, Riccati transformation, Differential equations, Quantum chemistry
Divisions:Life and Chemical Sciences > Institute of Organic Chemistry and Biochemistry > Collection of Czechoslovak Chemical Communications
Journal or Publication Title:Collection of Czechoslovak Chemical Communications
Volume:70
Number:7
Page Range:pp. 941-950
ISSN:0010-0765
E-ISSN:1212-6950
Publisher:Institute of Organic Chemistry and Biochemistry
Related URLs:
URLURL Type
http://dx.doi.org/10.1135/cccc20050941UNSPECIFIED
ID Code:2400
Item Type:Article
Deposited On:06 Feb 2009 17:18
Last Modified:06 Feb 2009 16:18

Citation

Kryachko, Eugene S. (2005) Notes on the Riccati Equation. Collection of Czechoslovak Chemical Communications, 70 (7). pp. 941-950. ISSN 0010-0765

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