Maupertuis Principle and Geodesic Equivalence

2004 ◽  
Keyword(s):  
Maupertuis Principle

scholarly journals Geometrization of the Schrödinger equation: Application of the Maupertuis Principle to quantum mechanics

2014 ◽  
Vol 11 (08) ◽  
pp. 1450066 ◽  
Author(s):  
Antonia Karamatskou ◽  
Hagen Kleinert
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Particle Density ◽  
Free Particle ◽  
Beltrami Operator ◽  
Classical Particle ◽  
Geometric Form ◽  
Curved Space ◽  
Maupertuis Principle ◽  
Semiclassical Expansion

In its geometric form, the Maupertuis Principle states that the movement of a classical particle in an external potential V(x) can be understood as a free movement in a curved space with the metric gμν(x) = 2M[V(x) - E]δμν. We extend this principle to the quantum regime by showing that the wavefunction of the particle is governed by a Schrödinger equation of a free particle moving through curved space. The kinetic operator is the Weyl-invariant Laplace–Beltrami operator. On the basis of this observation, we calculate the semiclassical expansion of the particle density.

scholarly journals Effective Hamiltonian dynamics via the Maupertuis principle

2020 ◽  
Vol 13 (4) ◽  
pp. 1395-1410
Author(s):  
Hartmut Schwetlick ◽  
◽  
Daniel C. Sutton ◽  
Johannes Zimmer ◽  
Keyword(s):  
Hamiltonian Dynamics ◽  
Effective Hamiltonian ◽  
Maupertuis Principle

scholarly journals On the principle of stationary isoenergetic action

2012 ◽  
Vol 91 (105) ◽  
pp. 63-81 ◽  
Author(s):  
Bozidar Jovanovic
Keyword(s):  
Symplectic Manifolds ◽  
Maupertuis Principle

We present several variants of the Maupertuis principle, both on the exact and the nonexact symplectic manifolds.

On Maupertuis principle in dynamics

2009 ◽  
Vol 63 (3) ◽  
pp. 331-346 ◽  
Author(s):  
Giovanni Romano ◽  
Raffaele Barretta ◽  
Annalisa Barretta
Keyword(s):  
Maupertuis Principle

scholarly journals The Jacobi-Maupertuis Principle in Variational Integrators

2009 ◽  
Author(s):  
Sujit Nair ◽  
Sina Ober-Blöbaum ◽  
Jerrold E. Marsden ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Variational Integrators ◽  
Maupertuis Principle
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