Duru-Kleinert transformation
Encyclopedia
The Duru-Kleinert transformation, named after İsmail Hakkı Duru
and Hagen Kleinert
, is a mathematical method for solving path integrals
of physical systems with singular potentials, which is necessary for the solution of all atomic path integrals due to the presence of Coulomb potentials (singular like
).
The Duru-Kleinert transformation replaces the diverging time-sliced path integral of Richard Feynman
(which thus does not exist) by a well-defined convergent one.
İsmail Hakkı Duru
İsmail Hakkı Duru is a Turkish theoretical physicist and professor of Mathematics at the Izmir Institute of Technology where he is dean of the science faculty.-Scholarships:NATO scholarship during B.S...
and Hagen Kleinert
Hagen Kleinert
Hagen Kleinert is Professor of Theoretical Physics at the Free University of Berlin, Germany , at theWest University of Timişoara, at thein Bishkek. He is also of the...
, is a mathematical method for solving path integrals
Path integral formulation
The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics...
of physical systems with singular potentials, which is necessary for the solution of all atomic path integrals due to the presence of Coulomb potentials (singular like
).The Duru-Kleinert transformation replaces the diverging time-sliced path integral of Richard Feynman
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...
(which thus does not exist) by a well-defined convergent one.
Papers
- H. Duru and H. KleinertHagen KleinertHagen Kleinert is Professor of Theoretical Physics at the Free University of Berlin, Germany , at theWest University of Timişoara, at thein Bishkek. He is also of the...
, Solution of the Path Integral for the H-Atom, Phys. Letters B 84, 185 (1979) - H. Duru and H. KleinertHagen KleinertHagen Kleinert is Professor of Theoretical Physics at the Free University of Berlin, Germany , at theWest University of Timişoara, at thein Bishkek. He is also of the...
, Quantum Mechanics of H-Atom from Path Integrals, Fortschr. d. Phys. 30, 401 (1982) - H. KleinertHagen KleinertHagen Kleinert is Professor of Theoretical Physics at the Free University of Berlin, Germany , at theWest University of Timişoara, at thein Bishkek. He is also of the...
, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets 3. ed., World Scientific (Singapore, 2004) (read book here)