LYCOS RETRIEVER 
Schrodinger Equation
built 605 days ago
The Schrodinger equation in 1-D is extended to 3-D in much the same way as the energy method in 1-D is extended to 2-D to deal with central-force motion. The kinetic-energy term associated with the angular variable(s) is written as a function of r and the angular momentum l, and is treated as a form of potential energy (the centrifugal potential energy). The resulting equation looks (somewhat in the case of the Schrodinger equation) like a 1-D problem with an "effective" potential energy. Although the program that finds energy levels and plots wavefunctions is itself very simple, its development involves a fair bit of detail (hint: skip to the program if you are not interested in detail).
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By AWT the Schrodinger equation describes the wave spreading in aether foam, where the mass density of foam is proportional to energy density (compare the increasing of soap foam density during shaking). By such way, each the energy wave is making the environment more dense, which in turn affects the wave spreading. The simple DHTML applet (for MSIE browser) or 2D Java applet illustrates such behavior.
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One key idea that was utilized by Erwin Schrodinger in arriving at his wave equation was the wave nature of matter. The concept of matter waves was proposed by Louis de Broglie in 1923. He understood the universal duality of wave and particle. He was able to show that a particle with momentum p will possess a wavelength given by h/p where h is the Planck's constant. Experimental confirmation soon followed. Scientist began to accept the wave particle duality of matter.
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The Schrodinger equation must be in one dimension only and the coordinate involved must correspond to a radial or length type coordinate. The potential must possess a minimum and at short distances it must be very large and positive (repulsive). The number of grid points must be a power of 2 due to the nature of the Fast Fourier Transform subroutine used.
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The Schrodinger equation is the name of the basic non-relativistic wave equation used in one version of quantum mechanics to describe the behaviour of a particle in a field of force. There is the time dependant equation used for describing progressive waves, applicable to the motion of free particles. And the time independent form of this equation used for describing standing waves.
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The Schrodinger equation for a multi-electron atom can be solved numerically, although Velectron-electron cannot be included as an explicit term in the Hamiltonian. Rather, its effect on can be accounted for by a mathematically simpler approach: that each electron interacts with an average of the nucleus + all other electrons (self-consistent field approximation).
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Schrodinger Equation