The coordinates of the center of mass [??] can be excluded from Hamiltonian (3) using Heisenberg's canonical transformation
Point canonical transformation
[2-4], dynamical group [5,6], factorization method , supersymmetric quantum mechanics, and shape invariance [8-10] are methods among many which were used in the search for exact solutions of wave function.
This form of the Hamiltonian resembles that of the simple harmonic oscillator, after a canonical transformation
with generating function F = ([[??].sub.0]/2) [q.sup.2] cot Q, where q and Q are the appropriate canonical variables.
A symplectic map M(t) is a canonical transformation
of a point in position-momentum phase space at initial time t = 0 to a point in position-momentum phase space at time t.
One might also wonder whether phase space is invariant under canonical transformation
. Canonical transformation
are those which keep the form of Hamiltonian's equation invariant.
We consider the canonical transformation
, specified by the generating function
Contracted Schrodinger equation topics include the purification of correlated and reduced density matrices, cumulants, extensivity and the connected formulation, generalized normal ordering, antihermitian formulations and canonical transformation
theory for dynamic correlations in multireference problems.
The authors have organized the main body of their text into ten chapters covering quantum field theory, path integral formulation, supersymmetric quantum mechanics, coherent and squeezed states, BerryAEs phase, Aharonov-Bohm, and Sagnac effects, phase space picture and canonical transformations
, and a wide variety of other related subjects.
Ozaktas, "Optimal filtering with linear canonical transformations
,"Optics Communications, vol.
We have adopted the method due to Markeev , in which the Hamiltonian function pertaining to the problem is made independent of time using several canonical transformations
. The existence of resonance and the stability of infinitesimal near the resonance frequency has been analyzed.
The topics include quantum mechanics in abstract Hilbert space, symmetries, higher-order processes, and canonical transformations
for quantum systems.
Sixteen papers from the June 2006 conference present new results in normal forms of Poisson structures, deformation of Poisson structures, reduction of systems with symmetry, Kontsevich formality and its variants, and quantization of canonical transformations
via their graphs.