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Topic: Schrodinger equation

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	Overview of Computational Chemistry
		Schroëdinger's equation eliminated this illogical quantum jump, replacing it with a transitional process in which the wave pattern gradually fades out, while the new wave pattern fades in, during which time light is being emitted.
		Schroëdinger's equation made it possible to resolve a variety of the inconsistencies that had been present in previous theories.
		Schroëdinger's equation is one of the starting points for most of the quantum chemical calculations that are done now, mostly using supercomputer technology.
	www.shodor.org /chemviz/overview/schroeq.html (1352 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)

	Schrödinger equation -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-10)
		This form of the Schrödinger equation is referred to as the Schrödinger wave equation.
		The operators A on the two sides of the equation are different things: the one on the right acts on kets, whereas the one of the left acts on scalar fields.
		This equation is the mathematical equivalent of (A measure of how likely it is that some event will occur) probability (Click link for more info and facts about conservation law) conservation law.
	www.absoluteastronomy.com /encyclopedia/s/sc/schr%f6dinger_equation.htm (1489 words)

	Self-Focusing In The Perturbed And Unperturbed Nonlinear Schrödinger Equation In Critical Dimension - Fibich, ... (Site not responding. Last check: 2007-10-10)
		0.6: Blow-Up for Schrödinger Equation with Pointwise Nonlinearity - Adami
		7 Self-Focusing in the Nonlinear Schrodinger Equation for Ultr..
		3 Focusing nonlinear Schrodinger equation and wave-packet coll..
	citeseer.ist.psu.edu /121090.html (1286 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)

	Schrodinger equation
		The Schrodinger equation plays the role of Newton's laws and conservation of energy in classical mechanics - i.e., it predicts the future behavior of a dynamic system.
		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.
	hyperphysics.phy-astr.gsu.edu /hbase/quantum/schr.html (463 words)

	[No title]
		The time-independent Schrodinger equation is then transformed from a Cartesian basis (x,y,z) to a basis of spherical polar coordinates (r, theta, phi).
		The resulting time-independent Schrodinger equation in spherical coordinates, with a potential dependent on only one coordinate V(r), is a partial differential equation that can however be separated into three different ordinary differential equations.
		This treatment of the Schrodinger equation yields the Rydberg formula for the energy levels and thus provides the Bohr model with a consistent physical basis.
	www.nat.vu.nl /~wimu/Schrod.html (1248 words)

	Report 2002
		The method is based on discretization of the time variable of the original equation with the help of Magnus expansion for evolution operator and subsequent approximation of this expansion by rational functions of stability [10].
		An analysis of relativistic field-theoretical equations was presented for photon-proton scattering reactions [12].
		A program [15] has been worked out for a numerical solution of the system of partial differential equations, describing the energy relaxation in the vicinity of an ion trajectory moving in a substance and in the field of a pulsed energy release stipulated by slowing down the ion beams in the substance.
	lit.jinr.ru /Reports/report_02/4e.html (1166 words)

	Hydrogen Schrodinger Equation (Site not responding. Last check: 2007-10-10)
		Since the equation must hold for all values of these variables, the collection of radial terms must be equal to a constant.
		Upon separation of the Schrodinger equation for the hydrogen atom, the radial equation is:
		In order to separate the equations, the radial part is set equal to a constant, and the form of the constant on the right above reflects the nature of the solution of the colatitude equation which yields the orbital quantum number.
	230nsc1.phy-astr.gsu.edu /hbase/quantum/hydrad.html (296 words)

	Hans Reichenbach [Internet Encyclopedia of Philosophy]
		and the equation H is a mathematical formulation of Heisenberg indeterminacy principle.
		Reichenbach explains the physical meaning of equation H. Equation H proves that the eigenvalues of position and momentum are different.
		Equation E2 can be expressed by the following statement: (AvB)#C, where A is "the electron goes through the first slit", B is "the electron goes through the second slit" and C is E2.
	www.iep.utm.edu /r/reichenb.htm (8071 words)

	Zoran Grujic - Home Page
		My research interests are mostly in nonlinear partial differential equations arising as mathematical models in fluid and plasma dynamics -- in particular, the Navier-Stokes equations (NSE), the MHD equations, the Euler equations, the Korteweg-de Vries- type equations (KdV-type), and the Schrodinger equations.
		A remark on time-analyticity for the Kuramoto-Sivashinsky equation (with I. Kukavica), Nonlinear Anal.
		Global solutions of the derivative Schrodinger equation in a class of functions analytic in a strip (with J.L. Bona and H. Kalisch) (submitted).
	www.math.virginia.edu /%7Ezg7c (408 words)

	Schrodinger's Equation
		The Schrödinger equation gives the kinetic energy plus the potential (a sum also known as the Hamiltonian H) of the wave function psi, which contains all the dynamical information about a system.
		For the time-independent case, energy is written at the operator -i hbar d/dt, and kinetic energy as the square of the momentum operator, i hbar Del, over 2m.
		Any attempt to shift the meaning of an equation as central to modern physics had first be able to regenerate all of its results.
	world.std.com /~sweetser/quaternions/quantum/schrodinger/schrodinger.html (1038 words)

	Schrodinger equation -- Encyclopædia Britannica
		The equation, developed (1926) by the Austrian physicist Erwin Schrödinger, has the same central importance to quantum mechanics as Newton's laws of motion have for the large-scale phenomena of classical mechanics.
		By replacing the energy E in equation () with a time-derivative operator, he generalized his wave equation to determine the time variation of the wave function as...
		To understand how a wave equation is used, it is helpful to think of an analogy with the vibrations of a bell, violin string, or drumhead.
	www.britannica.com /eb/article-9066220 (783 words)

	NUCLEAR GRAVITATION FIELD THEORY CHAPTER 7
		The Schrodinger Wave Equation, developed by Austrian theoretical physicist Erwin Schrodinger in 1925, defines the quantum mechanical characteristics of the electrons orbiting the nucleus and can be used to define the positions of the protons and neutrons within the “gravitational potential well of attraction” of the nucleus.
		The Classical Physics form of the Schrodinger Wave Equation is acceptable when applied to the electrons orbiting the nucleus because the velocities of the electrons are “non-relativistic.” The Classical Physics form of the Schrodinger Wave Equation may or may not be acceptable for evaluating the protons or neutrons bound to the nucleus of the atom.
		In this case, the Schrodinger Wave Equation is being used to determine the total energy of the electron orbiting the nucleus, by adding the Potential Energy and the Kinetic Energy of a particle.
	www.gravitywarpdrive.com /NGFT_Chapter_7.htm (2579 words)

	Schrodinger's Equation in General Relativity (Site not responding. Last check: 2007-10-10)
		Starting from Schrodinger's equation in comoving coordinates on an arbitrary four-manifold, a new method of deriving a relativistic generalization results in a fourth-order differential equation that reduces to the Klein-Gordon equation in the flat space limit.
		This equation, unlike the Klein-Gordon equation, involves the Ricci tensor, which appears naturally in the process of the derivation.
		Among the interesting features is the fact that the propagator of this equation falls off like the inverse fourth power of the momentum.
	flux.aps.org /meetings/YR97/BAPSAPR97/abs/S1280010.html (78 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.
		Schrodinger desired to develop a model that agreed with the experimental evidence.
		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)

	4aMUa3 On the use of Schrodinger's equation in the analytic determination (Site not responding. Last check: 2007-10-10)
		On the use of Schrodinger's equation in the analytic determination of horn reflectance.
		A change of variables transforms the equation into the form of the Schrodinger wave equation using in one-dimensional particle scattering.
		Boundary conditions can be derived directly from the physical dimensions of the horn, and the solution of the equation gives estimates of acoustic properties in terms of frequency dependent reflection and transmission coefficients.
	www.auditory.org /asamtgs/asa94aus/4aMUa/4aMUa3.html (238 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)

	Measurement in quantum mechanics FAQ: The Transactional Interpretation of Quantum Mechanics
		But for a massive particle you have to use the Schrodinger equation and if \Psi is a solution (OW), then \Psi* is not a solution.
		Remember that the CW must be time-reversed, and in general must be relativistically invariant; ie., a solution of the Dirac equation.
		Now (eg., see Bjorken and Drell, Relativistic QM), the nonrelativistic limit of that is not just the Schrodinger equation, but two Schrodinger equations: the time forward equation satisfied by \Psi, and the time reversed Schrodinger equation (which has i --> -i) for which \Psi* is the correct solution.
	www.mtnmath.com /faq/meas-qm-8.html (821 words)

	A Modulation Method For Self-Focusing In The Perturbed Critical Nonlinear Schrödinger Equation - Fibich, Papanicolaou ... (Site not responding. Last check: 2007-10-10)
		The modulation equations can be further simplified, depending on whether PNLS is power conserving or not.
		0.5: Self-Focusing In The Damped Nonlinear Schrödinger Equation - Fibich (2001)
		10: Self-focusing in the perturbed and unperturbed nonlinear Schrodinger equation in..
	citeseer.ist.psu.edu /228792.html (554 words)

	One-dimensional nonlinear Schrodinger equation: A nonlinear dynamical approach (Site not responding. Last check: 2007-10-10)
		We have studied a time-independent nonlinear Schrodinger equation of the tight-binding form on a one-dimensional lattice.
		For each case, an area-preserving map for the discrete nonlinear Schrodinger equation is introduced and analyzed.
		A ``stability-zone'' diagram, where the bounded orbits exist, is displayed in the parameter space, serving as ``phase diagram'' of the nonlinear Schrodinger equation under appropriate boundary conditions.
	cmp.ameslab.gov /cmp/Abstracts/soukoulis_36.html (187 words)

	The Schrodinger Wave Equation
		The purpose of this paper is to offer an introductory treatment of the differential equation the Schrodinger wave equation.
		By way of this, the historical developments that gave rise to this equation that is so integral to quantum physics will be addressed.
		Further, to illustrate the equation, the particle in a rigid box model is examined.
	online.redwoods.cc.ca.us /DEPTS/science/chem/storage/Schrod (1026 words)

	Visual Quantum Mechanics: Schrodinger Equation (Site not responding. Last check: 2007-10-10)
		When considering objects as small as electrons, the equivalent to Newton's Laws is an equation which was originally written down by Erwin Schrödinger.
		This equation cannot be derived from any fundamental law but is based on several well established principles of physics.
		Once the equation is set up for a particular situation, someone with an advanced math background or a computer can solve the equation.
	www.nhn.ou.edu /%7Ekieran/reuhome/vizqm/2schroeq.htm (129 words)

	Numerical schemes for the simulation of the two-dimensional Schrodinger equation using non-reflecting boundary ... (Site not responding. Last check: 2007-10-10)
		Numerical schemes for the simulation of the two-dimensional Schrodinger equation using non-reflecting boundary conditions.
		The construction of a hierarchy of high-frequency microlocal artificial boundary conditions for the two-dimensional linear Schr{\"o}dinger equation is proposed.
		These conditions are firstly derived for the half-space, the circular boundary and are next extended to a general arbitrarily-shaped boundary by using the techniques of pseudodifferential calculus.
	mip.ups-tlse.fr /publi/rapp02/02.36.html (159 words)

	Erwin Schrodinger - Atomic Magic (Site not responding. Last check: 2007-10-10)
		Schrodinger earned a doctorate at the University of Vienna in 1910.
		He succeeded (1927) Max Planck in the chair of theoretical physics at the University of Berlin but left Germany in 1933 because of Nazi threats--the same year he shared the Nobel Prize for physics with Paul Dirac for his contributions to atomic theory.
		Late in his life Schrodinger studied the foundations of physics and their implications for philosophy
	library.thinkquest.org /15567/bio/schrodinger.html (191 words)

	Topics in Quantum Dynamics
		Physicists are being taught in the course of their education rather early that every attempt at a sharp localization of a relativistic particle results in creation and annihilation processes.
		The Schrödinger equation describes time evolution of pure states of a quantum system, for instance evolution of pure states of a quantum particle, or of a many body system.
		Similarly for quantum mechanics: it is rather straightforward to construct generally covariant wave equations for Einstein`s relativity, while general covariance and geometrical meaning of the Schrödinger equation was causing problems, and it was not discussed in textbooks.
	www.cassiopaea.org /quantum_future/topics.htm (5212 words)

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