Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics Letters A

Derivation of the Hamiltonian form of the Klein-Gordon equation from Schrödinger-Fürth quantum diffusion theory

Morton D. Kostin

Published Dec 1, 1987• 4 citations
Publisher
DOI
10.1016/0375-9601(87)90183-6

Related papers

Derivation of the Hamiltonian form of the Klein-Gordon equation from Schrödinger-Furth quantum diffusion theory: Comments

Suresh Chandra Tiwari

Physics Letters A•Nov 1, 1988•11 citations

Klein-Gordon Equation within the Real Hilbert Space Formalism

Sergio Giardino, Cristiano Rosa

•Jan 1, 2025•0 citations

Derivation of both Klein-Gordon equation and Time Dependent Schrödinger Equation form classical wave function

Mobarak Tag, Wail Hessen ALawad, Adil Elrayah +1 more

In this study, both the Klein-Gordon equation and time-dependent Schrodinger equation are directly derived from De Broglie's (\lamda=h/p). Besides that, a new formula of the Klein-Gordon equation was obtained by using two equations, i.e., the classical wave function and relativistic total energy relation [[hw] = [(h^2 k^2)/2m] + V]. Moreover, a new equation of time-dependent Schrodinger (TDSE) in three-dimension 3D was derived and evidently obtained. Thus, the previous result corresponds to (TDSE) in 3D calculated using two equations, (i.e., Einstein energy and Newton's second law of mechanics).

Journal of Karary University for Engineering and Science•Oct 14, 2022•0 citations

Relativistic Schrödinger Equation

Z. Ficek

This chapter introduces the concepts of the relativistic theory to basic problems of quantum physics, in particular, the extension of the Schrodinger equation to a relativistic form. Starting from the fundamental laws of relativity, the chapter evaluates the Klein–Gordon equation and investigates if the equation can be considered a generalization of the non-relativistic Schrodinger equation to the case of the relativistic energy. The chapter shows that the wave function, which is a solution to the Klein–Gordon equation, cannot be connected with the probability wave function. For this reason, the Dirac equation is used to solve the problems faced by the Klein–Gordon equation. The Dirac equation also includes the spin. The advantage of the Dirac equation over the Schrodinger and Klein–Gordon equations is that it naturally includes the spin. In the Schrodinger and Klein–Gordon equations, the spin is not present and has to be added to the wave function manually whenever the wave function determines a system with the spin.

•Mar 3, 2017•0 citations

Klein–Gordon equation within the real Hilbert space formalism

Cristiano Rosa, Sergio Giardino

arXiv:2510.16602•Annals of Physics•Oct 21, 2025•2 citations

From Classical Hamiltonian Flow to Quantum Theory: Derivation of the Schrödinger Equation

Gerhard Grössing

arXiv:quant-ph/0311109•Foundations of Physics Letters•Jul 22, 2004•34 citations
In this study, both the Klein-Gordon equation and time-dependent Schrodinger equation are directly derived from De Broglie's (\lamda=h/p). Besides that, a new formula of the Klein-Gordon equation was obtained by using two equations, i.e., the classical wave function and relativistic total energy relation [[hw] = [(h^2 k^2)/2m] + V]. Moreover, a new equation of time-dependent Schrodinger (TDSE) in three-dimension 3D was derived and evidently obtained. Thus, the previous result corresponds to (TDSE) in 3D calculated using two equations, (i.e., Einstein energy and Newton's second law of mechanics).
This chapter introduces the concepts of the relativistic theory to basic problems of quantum physics, in particular, the extension of the Schrodinger equation to a relativistic form. Starting from the fundamental laws of relativity, the chapter evaluates the Klein–Gordon equation and investigates if the equation can be considered a generalization of the non-relativistic Schrodinger equation to the case of the relativistic energy. The chapter shows that the wave function, which is a solution to the Klein–Gordon equation, cannot be connected with the probability wave function. For this reason, the Dirac equation is used to solve the problems faced by the Klein–Gordon equation. The Dirac equation also includes the spin. The advantage of the Dirac equation over the Schrodinger and Klein–Gordon equations is that it naturally includes the spin. In the Schrodinger and Klein–Gordon equations, the spin is not present and has to be added to the wave function manually whenever the wave function determines a system with the spin.