scholarly journals Classical canonical transformation theory as a tool to describe multidimensional tunnelling in reactive scattering. Hopping method revisited and collinear H+H2 exchange reaction near the classical threshold

1999 ◽  
Vol 1 (6) ◽  
pp. 1071-1079 ◽  
Author(s):  
Gennady V. Mil'nikov ◽  
António J. C. Varandas
Keyword(s):  
Exchange Reaction ◽  
Canonical Transformation ◽  
Reactive Scattering ◽  
Transformation Theory

scholarly journals Theory of Generalized Canonical Transformations for Birkhoff Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yi Zhang
Keyword(s):  
Canonical Transformation ◽  
Natural Generalization ◽  
Analytical Mechanics ◽  
Hamiltonian Mechanics ◽  
Canonical Transformations ◽  
Transformation Theory ◽  
Special Cases ◽  
Criterion Equation ◽  
Important Means ◽  
Transformation Formulas

Transformation is an important means to study problems in analytical mechanics. It is often difficult to solve dynamic equations, and the use of variable transformation can make the equations easier to solve. The theory of canonical transformations plays an important role in solving Hamilton’s canonical equations. Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics. This paper attempts to extend the canonical transformation theory of Hamilton systems to Birkhoff systems and establish the generalized canonical transformation of Birkhoff systems. First, the definition and criterion of the generalized canonical transformation for the Birkhoff system are established. Secondly, based on the criterion equation and considering the generating functions of different forms, six generalized canonical transformation formulas are derived. As special cases, the canonical transformation formulas of classical Hamilton’s equations are given. At the end of the paper, two examples are given to illustrate the application of the results.

scholarly journals Canonical transformation theory from extended normal ordering

2007 ◽  
Vol 127 (10) ◽  
pp. 104107 ◽  
Author(s):  
Takeshi Yanai ◽  
Garnet Kin-Lic Chan
Keyword(s):  
Canonical Transformation ◽  
Transformation Theory ◽  
Normal Ordering

scholarly journals Quadratic canonical transformation theory and higher order density matrices

2009 ◽  
Vol 130 (12) ◽  
pp. 124102 ◽  
Author(s):  
Eric Neuscamman ◽  
Takeshi Yanai ◽  
Garnet Kin-Lic Chan
Keyword(s):  
Canonical Transformation ◽  
Higher Order ◽  
Transformation Theory ◽  
Density Matrices

Optically assisted H + H2 exchange reaction and reactive scattering resonances

1990 ◽  
Vol 173 (2-3) ◽  
pp. 169-174 ◽  
Author(s):  
Tamar Seideman ◽  
Jeffrey L. Krause ◽  
Moshe Shapiro
Keyword(s):  
Exchange Reaction ◽  
Reactive Scattering ◽  
Scattering Resonances
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