Time-independent Schrodinger equation in real-space is an indispensable
element of introductory quantum mechanics. In contrast, Schrodinger equation in
momentum space, being an integral equation not readily amenable to an
analytical solution, is a rarity in the quantum mechanics pedagogy. In this
tutorial, we present a numerical approach to the Schrodinger equation in
momentum space. After a suitable discretization process, we obtain the
Hamiltonian matrix that is numerically diagonalized. By considering a few
examples, we show that this method is ideal for exploring bound-states in a
localized potential in one or higher dimensions, and it complements the
traditional (analytical or numerical) treatment of Schrodinger equation in
real-space.
martes, 6 de octubre de 2009
Numerical approach to Schrodinger equation in momentum space. (arXiv:0910.0574v1 [physics.comp-ph])
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The solution to the time-dependent relative quantum Schrodinger equation for one atom is a basic need for research at the femtotechnical level. That resolution of electron scale structural features such as energy and force fields or thermic tint is necessary for topological analysis of the data horizon of picotechnical molecular or material features. Recent research has produced the picoyoctometric, 3D, interactive video atomic model function. This system graphs the atomic data point image in terms of chronons and spacons for exact quantized relativistic animation.
ResponderEliminarElectron transport and related features of biomolecular science have femtoscale topological functionality. That dimension has data density which exponentiates the progress achievable in research. The atomic topological function determines that, since it's picoyoctoscale data generates the femtostructural horizon which holds the solutions to biomolecular quantum effects or relativistic factors in analysis or design work.
The atom's RQT (relative quantum topological) data point imaging function is built by combination of the relativistic Einstein-Lorenz transform functions for time, mass, and energy with the workon quantized electromagnetic wave equations for frequency and wavelength. The atom labeled psi (Z) pulsates at the frequency {Nhu=e/h} by cycles of {e=m(c^2)} transformation of nuclear surface mass to forcons with joule values, followed by nuclear force absorption. This radiation process is limited only by spacetime boundaries of {Gravity-Time}, where gravity is the force binding space to psi, forming the GT integral atomic wavefunction. The expression is defined as the series expansion differential of nuclear output rates with quantum symmetry numbers assigned along the progression to give topology to the solutions.
Next, the correlation function for the manifold of internal heat capacity particle 3D functions condensed due to radial force dilution is extracted; by rearranging the total internal momentum function to the photon gain rule and integrating it for GT limits. This produces a series of 26 topological waveparticle functions of five classes; {+Positron, Workon, Thermon, -Electromagneton, Magnemedon}, each the 3D data image of a type of energy intermedon of the 5/2 kT J internal energy cloud, accounting for all of them.
Those values intersect the sizes of the fundamental physical constants: h, h-bar, delta, nuclear magneton, beta magneton, k (series). They quantize nuclear dynamics by acting as fulcrum particles. The result is the picoyoctometric, 3D, interactive video atomic model data imaging function, responsive to keyboard input of virtual photon gain events by relativistic, quantized shifts of electron, force, and energy field states and positions.
Images of the h-bar magnetic energy waveparticle of ~175 picoyoctometers are available online at http://www.symmecon.com with the complete RQT atomic modeling guide titled The Crystalon Door, copyright TXu1-266-788. TCD conforms to the unopposed motion of disclosure in U.S. District (NM) Court of 04/02/2001 titled The Solution to the Equation of Schrodinger.
(C) 2009, Dale B. Ritter, B.A.