2023Unpublished venueOpen access

Derivation of a Riccati Form equation from the Klein-Gordon equation and its solution

Alessandro Vita

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Abstract

This work was conducted independently. In this article, we explore the transformation of the Klein-Gordon equation, a second-order relativistic partial differential equation, into a Riccati equation. This transformation is achieved by assuming a specific form for the wave function and introducing a new function that allows us to rewrite the equation in the Riccati form. In the last part we try to solve the Riccati equation derived. The implications and applications of this transformation are discussed briefly.This work was conducted independently.

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What this paper is about

This work was conducted independently. In this article, we explore the transformation of the Klein-Gordon equation, a second-order relativistic partial differential equation, into a Riccati equation. This transformation is achieved by assuming a specific form for the wave function and introducing a new function that allows us to rewrite the equation in the Riccati form. In the last part we try to solve the Riccati equation derived. The implications and applications of this transformation are discussed briefly.This work was conducted independently.

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Available abstract

This work was conducted independently. In this article, we explore the transformation of the Klein-Gordon equation, a second-order relativistic partial differential equation, into a Riccati equation. This transformation is achieved by assuming a specific form for the wave function and introducing a new function that allows us to rewrite the equation in the Riccati form. In the last part we try to solve the Riccati equation derived. The implications and applications of this transformation are discussed briefly.This work was conducted independently.

Key concepts: Riccati equation, Algebraic Riccati equation, Transformation (genetics), First-order partial differential equation, Klein–Gordon equation, Partial differential equation, Mathematics, Function (biology)

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