منابع مشابه
General Quantum Surface of Section Method
A new method for exact quantization of general bound Hamiltonian systems is presented. It is the quantum analogue of the classical Poincaré Surface Of Section (SOS) reduction of classical dynamics. The quantum Poincaré mapping is shown to be the product of the two generalized (non-unitary but compact) on-shell scattering operators of the two scattering Hamiltonians which are obtained from the o...
متن کاملQuantum Surface of Section Method: Eigenstates and Unitary Quantum Poincaré Evolution
The unitary representation of exact quantum Poincaré mapping is constructed. It is equivalent to the compact representation [19, 22, 23] in a sense that it yields equivalent quantization condition with important advantage over the compact version: since it preserves the probability it can be literally interpreted as the quantum Poincaré mapping which generates quantum time evolution at fixed en...
متن کاملSemiclassical quantization using Bogomolny's quantum surface of section.
The efficacy and accuracy of Bogomolny’s method of the quantum surface of section is evaluated by applying it to the quantization of the motion of a particle in a smooth 2-D potential. This method defines a transfer operator T in terms of classical trajectories of one Poincaré crossing; knowledge of T provides information about the eigenstates of the quantum system. By using a more robust quant...
متن کاملEnergy Spectrum and Eigenfunctions through the Quantum Section Method
We present the Quantum Section Method as a quantization technique to compute the eigenvalues and the eigenfunctions of quantum systems. As an instructive example we apply this procedure to quantize the annular billiard. The method uses the symmetry of the system to determine an auxiliary section separating the system into partial regions and computes the Green's functions for Schroedinger's equ...
متن کامل8 v 1 8 F eb 1 99 5 Quantum Surface of Section Method : Decomposition of the Resolvent ( E − Ĥ ) −
The paper presents exact surface of section reduction of quantum mechanics. The main theoretical result is a decomposition of the energy-dependent propagator Ĝ(E) = (E − Ĥ) in terms of the propagators which (also or exclusively) act in Hilbert space of complex-valued functions over the configurational surface of section, which has one dimension less than the original configuration space. These ...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1995
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/28/14/029