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Topic: Schrodinger wave equation

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	Propability wave and indeterminacy principle
		In the hydrogen atom the waves of matter were dense in the places where the orbits described by the Bohr theory were situated.
		Schrodinger the radiuses of orbits and the placement of the spectral lines of many other than hydrogen chemical elements can be calculated.
		According to the Schrodinger equation some part of the wave of electron goes through the barrier and some part is reflected.
	library.thinkquest.org /19662/low/eng/indeterminate.html (1181 words)

	\| International School of Photonics \| ISP Archives \| ISP Article Collection \|
		Erwin Schrodinger, discoverer of wave mechanics was deeply influenced by the philosophical wisdom of the East.
		The wave equation derived by Schrodinger is universally recognized as one of the greatest achievements of the 20th century physics.
		Schrodinger was well versed in the techniques of Bhagavat Gita and he knew that he was a "Jnanayogi.".
	www.photonics.cusat.edu /article2.html (1250 words)

	Lewis Little's Theory of Elementary Waves
		If the waves meet when both are at their crest the resultant wave of their combination is larger than the sum of the originals.
		So the ghost-like packets of waves in the standard theory have been replaced by a real existent, and the behavior of that wave is contrary to standard interpretation - the wave moves in reverse, from the target, or more generally from the detector, towards the source.
		The wave itself is moving from the detector to the source; no dynamic information propagates through the wave; the wave carries the information as it moves.
	www.objectivescience.com /articles/waves1.htm (3230 words)

	Back Action Paper
		The recombination of the waves from both slits exerts a quantum force on the particle whose effects exactly reproduce the observed statistical coherent wave patterns for ensembles of particles whose initial positions are postulated to obey the Born probability rule.
		These nonlinearities in the Schrodinger equation which are generically induced in mean-field approximations to many-particle effects are swept away by second-quantizing the wavefunction so that it is now a creation and destruction operator of elementary excitations of collective modes in non-relativistic solid state physics.
		If we accept the postulate that the quantum wave is "pre-mind", then the direct affect of the particles of matter on their attached wave is a change in that wave that is an internal representation or map of the material environment in the sense of models of artificial intelligence.
	www.qedcorp.com /pcr/pcr/qmback.html (3655 words)

	Quantum Mechanics 1
		When Born showed that the solution of Schrodinger's wave equation could be interpreted as a non-observable object used only as an intermediary to calculate relative probabilities of the various allowed outcomes of an experiment, and when Bohr and Heisenberg solidified this interpretation (the so-called "Copenhagen interpretation") Schrödinger objected strongly.
		Whatever the correct wave equation might be, it should contain the relations between wave and particle properties that seem to apply for particles (or waves) moving freely through space.
		Solutions of the wave equation in the e-m case are the E and B fields of the wave.
	www.phy.duke.edu /courses/100/lectures/QM1/QM1.html (1249 words)

	Schrodinger equations - DispersiveWiki
		The perturbative theory of nonlinear Schrodinger equations (and the semilinear Schrodinger equations in particular) rests on a number of linear and nonlinear estimates for the free Schrodinger equation.
		A nonlinear Schrodinger equation with nonlinearity of degree 4 is a quartic nonlinear Schrodinger equation.
		This is the Schrodinger counterpart of the wave maps equation.
	tosio.math.toronto.edu /wiki/index.php/Schrodinger_equations (412 words)

	Erwin Schrodinger
		Schrodinger was an unconventional man. Throughout his life he traveled with walking-boots and rucksack and for this he had to face some difficulty in gaining entrance to the Solvay Conference for Nobel laureates.
		Schrodinger’s wave equation was the second theoretical explanation for the movement of electrons in an atom, the first being Werner Heisenberg’s matrix mechanics.
		Schrodinger was deeply moved, but in the end it was a personal appeal from Planck that persuaded him to accept the Berlin offer; as the result of doing so he automatically became a German national.” Before taking up the appointment at Berlin, Schrodinger traveled to Brussels to attend the Solvay physics conferences.
	www.vigyanprasar.gov.in /scientists/ESchrodinger.htm (3464 words)

	The Schrodinger Equation
		The complex form of the equation describing a wave is used for mathematical convenience in the sections on ellipsometry, but the complex form is a necessity here.
		The equation says that the second derivative of Y with respect to x is equal to a function of x and Y.
		In the Schrodinger equation, the curvature is proportional to the magnitude of the function, so Y(x) flattens out as it approaches the axis, and for an appropriate value of E the approach to the axis will be asymptotic.
	www.kw.igs.net /~jackord/bp/i4.html (1385 words)

	The Schrodinger Wave Equation
		Further, to illustrate the equation, the particle in a rigid box model is examined.
		The troubling dichotomy of waves and particle of light quanta cannot be escaped.
		It is replete throughout nature: in packets of light quanta, photons; in subatomic particles such as electrons and protons; in the flight of a baseball; in the orbit of a planet.
	online.redwoods.cc.ca.us /DEPTS/science/chem/storage/Schrod/index.htm (1026 words)

	Schrodinger equation
		It is a wave equation in terms of the wavefunction which predicts analytically and precisely the probability of events or outcome.
		The Schrodinger equation gives the quantized energies of the system and gives the form of the wavefunction so that other properties may be calculated.
		The idealized situation of a particle in a box with infinitely high walls is an application of the Schrodinger equation which yields some insights into particle confinement.
	hyperphysics.phy-astr.gsu.edu /hbase/quantum/schr.html (463 words)

	Schrödinger wave equation
		Equation (5) is called the Schrödinger wave equation.
		From a mathematical point of view, this equation is a second-order linear differential equation with nonlinear coefficients for a complex function F(r, t).
		The time-independent wave function y(r) and its derivatives with respect to space coordinates must be continuous.
	www.mtmi.vu.lt /pfk/funkc_dariniai/quant_mech/schrodinger.htm (241 words)

	The Quantum Atom
		In contrast to Heisenberg, Schrodinger's development used conventional and readily understood (at least by the physicists and mathematicians of his day) wave equations.
		It was finally recognized that this equation may be used to give the probability of finding the electron in a given region of space.
		Schrodinger's wave equation involved three "constants" called quantum numbers that were used to exactly assign the energy level, orbital, and direction of the electron.
	neon.chem.uidaho.edu /~honors/schrod.html (1542 words)

	What is the Schrodinger equation, and how is it used?
		The eigenvalues of the wave equation were shown to be equal to the energy levels of the quantum mechanical system, and the best test of the equation was when it was used to solve for the energy levels of the Hydrogen atom, and the energy levels were found to be in accord with Rydberg's Law.
		Schrodinger's equation shows all of the wave like properties of matter and was one of greatest achievements of 20th century science.
		Answered by: Simon Hooks, Physics A-Level Student, Gosport, UK 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.
	www.physlink.com /Education/AskExperts/ae329.cfm (578 words)

	Schrodinger's Wave Equation (Site not responding. Last check: 2007-09-10)
		The wave funcition Psi(x,t) is initially a guassian wave packet moving to the right.
		The boundary conditions are periodic, so that waves which exit to the right will return on the left.
		The algorithm for integrating the Schrödinger wave equation is from: Richardson, John L., Visualizing quantum scattering on the CM-2 supercomputer, Computer Physics Communications 63 (1991) pp 84-94
	www.math.sunysb.edu /~ccc/WaveSim.html (91 words)

	The Schrodinger Wave Equation -- Page 2
		Schrodinger, an Austrian physicist noted for his work on the physics of strings, took flight to a villa in the Swiss Alps in 1925, leaving his wife behind and gathering a former Viennese girlfriend.
		Therefore, the wave equation corresponding to the particle in the box is given by
		Gasping for breath, we at last have unearthed the solution to the wave equation for the particle of the nth quantum state in the rigid box.
	online.redwoods.cc.ca.us /DEPTS/science/chem/storage/Schrod/page2.htm (695 words)

	The Hydrogen Atom
		The de Broglie wavelength for the matter wave corresponding to a particle with momentum p is l = h/p, and if we stipulate that the circumference 2pr of a circular orbit of radius r must be an integer multiple of the wavelength, we have 2pr/l = 2prp/h = n for some positive integer n.
		It arises from an analysis of the purely radial component of the Schrodinger wave equation of the ground state, which is spherically symmetrical and has an angular quantum number of zero.
		The superiority of the wave mechanical model of the hydrogen atom over Bohr's model is immense, because it not only duplicates and (in a sense) "explains" the quantized energy levels, it actually gives the complete probability density functions for the various possible stationary states.
	www.mathpages.com /home/kmath538/kmath538.htm (2153 words)

	[No title]
		The solution of the Schrodinger equation for the hydrogen atom is a formidable mathematical problem, but is of such fundamental importance that it will be treated in outline here.
		The Schrodinger equation for an exactly solvable 2-D interacting oscillator problem is solved numerically by application of a parallel genetic algorithm on a fixed coordinate grid (n x n).
		Using the Schrodinger equation, which describes the structures of actual atoms, they found that the electron orbits do arrange themselves into a hierarchy of quantized energy levels, although in a configuration somewhat different from that of an actual atom.
	www.lycos.com /info/schrodinger-equation.html (366 words)

	[No title]
		The wave function is displayed in a variety of ways, and the transmission and reflection probabilities are computed.
		The computations are done by numerically integrating the Schrodinger equation from the region of the transmitted wave, where the wave function is known up to some overall normalization and phase, to the region of the incident wave.
		F36.079 Qualitative features of 1D Schrodinger equation with an asymmetric Coulomb potential in the study of an impurity at the boundary of different quantum wires.
	www.lycos.com /info/schrodinger-equation--potentials.html (348 words)

	Quantum Motion
		However, the non-relativistic Schrodinger equation for a particle in a classical potential force field emerges only in the approximation that there is no direct back-reaction of the particle on its guiding wave function.
		The classical mechanics equations of motion are defined from a classical action (I) which is the path integral of the Lagrangian (L) with respect to the time differential (dt) for a given trajectory determined by given position (q(t)) and velocity(dq(t)/dt) functions of the time.
		The uncertainty relation for a wave packet from Fourier analysis is shown to be a condition for destructive interference between a wave of number k and one of k + &k/2 at the edge of the packet.
	www.qedcorp.com /pcr/pcr/qmotion.html (18595 words)

	[No title]
		It had already been shown that light behaved as a wave and was able to be defracted and refracted.
		Thus the wavelength of the "particle wave" is related to the momentum of the particle.
		This is the differential form of Schrodinger’s equation.
	www.ldolphin.org /studynotes/relativ/quantum/index.htm (1307 words)

	Modern Theory of Atomic Structure, page 2
		Schrodinger found that three variables, called quantum numbers, would help establish specific aspects of electron behavior.
		The Schrodinger Wave Equation is the foundation of the Modern Theory of Atomic Structure.
		It is known as a wave-mechanical equation because it treats the electron as both a wave and a particle.
	www.bcpl.net /~kdrews/mtas/modern2.html (1095 words)

	Schrodinger's Equation
		The wave description of de Broglie is not adequate to explain the properties of the electron under different types of external potential fields.
		This very important equation is a result of conservation of energy and the relations between total energy and w and between the momentum and the wave number, k.
		The last equation reduces to two equations: one for the real part and one for the imaginary part.
	www.missioncollege.org /depts/physics/P4poe/P4D/Schrodinger.htm (1139 words)

	Schrodinger equation
		For other problems, the potential U(x) serves to set boundary conditions on the spatial part of the wavefunction and it is helpful to separate the equation into the time-independent Schrodinger equation and the relationship for time evolution of the wavefunction
		The operation of the Hamiltonian on the wavefunction is the Schrodinger equation.
		Solutions exist for the time-independent Schrodinger equation only for certain values of energy, and these values are called "eigenvalues" of energy.
	hyperphysics.phy-astr.gsu.edu /hbase/quantum/scheq.html (529 words)

	The Quantum Wave Equation
		The only parameters in the final form of the equation are the width L of the well and the ground state period.
		In the example, one has three choices for the initial wavefunction, and can generate its time dependence either directly using the Schrodinger equation or indirectly using FFSS and the dispersion relation (frequency is proportional to square of quantum number).
		The direct numerical solution of the Schrodinger equation, even with 300 time steps between each of the plotted 640 frames, cannot be expected to give results as accurate as the FFSS over an extended period of time.
	www.kw.igs.net /~jackord/bp/n4.html (1510 words)

	Nuclear Gravitation Field Theory
		By combining and analyzing the principles of Electrostatics, Isaac Newton’s Law of Gravity, Quantum Mechanics, and Einstein’s General Theory of Relativity, I demonstrate both qualitatively and quantitatively that the “Strong Nuclear Force” that holds the protons and neutrons together in the nucleus is the same force as Gravity.
		This analysis qualitatively evaluates the Schrodinger Wave Equation with the Nuclear Gravitation Field as the Potential Function established by the mass of the nucleus of the atom using Newton’s Law of Gravity.
		With the Nuclear Gravitation Field as the Potential Function in the Schrodinger Wave Equation, the Schrodinger Wave Equation must be modified to include the “Space-Time Compression” effects of General Relativity because of the intensity of the quantized Nuclear Gravitation Field.
	www.physicsforums.com /showthread.php?t=17526 (672 words)

	[No title]
		For this Elastic Continuum the equilibrium equations of elasticity are identical with vector wave equation of Maxwell's electromagnetic theory.
		For this ‘Elastic Continuum’ the equilibrium equations of elasticity are found to be identical with the vector wave equation of Maxwell’s electromagnetic theory.
		Particular solutions of these equilibrium equations as functions of space-time coordinates, satisfying appropriate boundary and stability conditions within a bounded region, are shown to represent various ‘strain bubbles’ or elementary particles and the electromagnetic fields.
	www.geocities.com /gssandhu_1943/index.html (2322 words)

	[No title]
		Introduction and Motivation Certainly, there is no lack of books with discussions of quantum mechanics in the world today, but the vast majority relegate the discussion of the time-dependent properties of the wave equation to little more than a footnote.
		The study of the time-dependent Schrodinger equation is in fact a study of parabolic partial differential equations, and although such research may not be full of mind boggling counter-intuitive results, it is at least mathematically significant.
		The FTCS method provides a perfectly viable solution to the Schrodinger equation, but we have not yet considered the circumstances under which this solution remains well behaved.
	wwwrel.ph.utexas.edu /Public/Students/onager/TermPaper.doc (352 words)

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