The coordinates of the center of mass [??] can be excluded from Hamiltonian (3) using Heisenberg's
canonical transformation [43]:
Point
canonical transformation [2-4], dynamical group [5,6], factorization method [7], 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 [21], 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.