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Topic: Perturbation theory (quantum mechanics)

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	Quantum Theory - Mechanics - Crystalinks
		Quantum mechanics is a fundamental branch of theoretical physics that replaces Newtonian mechanics and classical electromagnetism at the atomic and subatomic levels.
		Quantum mechanics is a more fundamental theory than Newtonian mechanics and classical electromagnetism, in the sense that it provides accurate and precise descriptions for many phenomena that these "classical" theories simply cannot explain on the atomic and subatomic level.
		The quantum theory of the atom developed as an explanation for the electron's staying in its orbital, which could not be explained by Newton's laws of motion and by classical electromagnetism.
	www.crystalinks.com /quantumechanics.html (4216 words)

	Search Results for Quantum
		Quantum mechanics was very fortunate indeed to attract, in the very first years after its discovery in 1925, the interest of a mathematical genius of von Neumann's stature.
		The quantum theory paper explained that the Stark effect, namely the splitting of the spectral lines of hydrogen by an electric field (the amount being proportional to the field strength), could be proved from the postulates of quantum theory.
		For a given value of the principal quantum number is the number of energy levels of a single electron in the alkali metal spectra in an external magnetic field the same as the number of electrons in the closed shell of the rare gases which corresponds to this principal quantum number.
	www-groups.dcs.st-and.ac.uk /~history/Search/historysearch.cgi?SUGGESTION=Quantum&CONTEXT=1 (15284 words)

	Quantum field theory - Cetin BAL - GSM:+90 05366063183 -Turkey/Denizli
		Quantum field theory originated in the problem of computing the power radiated by an atom when it dropped from one quantum state to another of lower energy.
		As described in the article on identical particles, quantum mechanical particles of the same species are indistinguishable, in the sense that the state of the entire system must be symmetric (bosons) or antisymmetric (fermions) when the coordinates of its constituent particles are exchanged.
		Quantum field theory was created by Dirac when he attempted to quantize the electromagnetic field in the late 1920s.
	www.zamandayolculuk.com /cetinbal/quantumalankuram.htm (3755 words)

	Quantum Gravity
		Quantum Gravity is reputed to be one of the most difficult puzzles of science.
		In 1955 John Wheeler argued that when you combine general relativity and quantum mechanics you will have a theory in which the geometry of space-time is subject to quantum fluctuations, He computed that these fluctuations would become significant if you could look at space-time on length scales as small as the Planck length.
		Although there is no direct empirical input into quantum gravity, physicists hope to accomplish unification by working on the requirement that there must exist a mathematically self consistent theory which accounts for both general relativity and quantum mechanics as they are separately confirmed experimentally.
	www.weburbia.demon.co.uk /pg/qugrav.htm (4347 words)

	String theory
		perturbation theory; the quantum mechanics of branes (higher dimensional objects than strings) is not understood; the behaviour of string theory in cosmological settings (time-dependent backgrounds) is still being worked out; finally, the principle by which string theory selects its
		By applying the ideas of quantum mechanics to strings it is possible to deduce the different vibrational modes of strings, and that each vibrational state appears to be a different particle.
		Yang-Mills theory on the four-dimensional boundary of the
	schools-wikipedia.org /wp/s/String_theory.htm (5172 words)

	List of publications (compact version)
		Sergeev A. and Sherstyuk A. High-order perturbation theory for the bound states of the Dirac-equation with a Yukawa-type potential.
		Sergeev A. and Goodson D. Semiclassical self-consistent-field perturbation theory for the hydrogen atom in a magnetic field.
		Popov and A. Sergeev (1998): Ionization of atoms in weak fields and the asymptotic behavior of higher-order perturbation theory.
	www.asergeev.com /files/appls/publicat.htm (925 words)

	Quantum mechanics Encyclopedia (Site not responding. Last check: )
		Quantum mechanics is a fundamental branch of theoretical physics with wide applications in experimental physics that replaces classical mechanics and classical electromagnetism at the atomic and subatomic levels.
		Quantum mechanics is a more fundamental theory than Newtonian mechanics and classical electromagnetism, in the sense that it provides accurate and precise descriptions for many phenomena that these "classical" theories simply cannot explain on the atomic and subatomic level.
		In the formalism of quantum mechanics, the state of a system at a given time is described by a complex wave function (sometimes referred to as orbitals in the case of atomic electrons), and more generally, elements of a complex vector space.
	www.hallencyclopedia.com /Quantum_mechanics (8055 words)

	Perturbation theory (quantum mechanics) (Site not responding. Last check: )
		In the theory of quantum electrodynamics (QED), in which the electron-photon interaction is treated perturbatively, the calculation of the electron's magnetic moment has been found to agree with experiment to eleven decimal places.
		In quantum chromodynamics, for instance, the interaction of quarks with the gluon field cannot be treated perturbatively at low energies because the coupling constant (the expansion parameter) becomes too large.
		Perturbation theory also fails to describe states that are not generated adiabatically from the "free model", including bound states and various collective phenomena such as solitons.
	www.guideofpills.com /Perturbation_theory_(quantum_mechanics).html (2379 words)

	Perturbation theory: Encyclopedia II - Perturbation theory - Simple example
		Regular perturbation theory may only be used to find those solutions of a problem that evolve smoothly out of the initial solution when changing the parameter (that are "adiabatically connected" to the initial solution).
		A well known example from physics where regular perturbation theory fails is in fluid dynamics when one treats the viscosity as a small parameter.
		Perturbation theory can fail when the system can go to a different "phase" of matter, with a qualitatively different behaviour that cannot be understood by perturbation theory (e.g., a solid crystal melting into a liquid).
	www.experiencefestival.com /a/Perturbation_theory_-_Simple_example/id/5372701 (774 words)

	The search for a Quantum Field Theory
		Quantum Field Theory purports to be the most fundamental of sciences in that it concerns the ultimate constituents of matter.
		General Relativity is like quantum mechanics in that it is not so much a theory as a whole way of thinking, and it can be very hard to fit something as grandiose as this with other frameworks, quantum mechanics in particular.
		Quantum chromodynamics, the gauge theory of quark colour is the candidate theory of the binding force, but we are limited by the fact that bound states cannot be done satisfactorily with quantum field theory.
	www.cgoakley.demon.co.uk /qft (6196 words)

	Linux4Chemistry - Linux software for chemistry: molecular modeling, visualization, graphic, quantum mechanic, dynamic, ...
		MacroModel is a molecular modeling software package which allows the user to construct and graphically manipulate both simple and complex chemical structures, to apply molecular mechanics and dynamics techniques to evaluate the energies and geometries of molecules in vacuo or in solution, and to display and examine graphically the results of the modeling calculations.
		MOPAC2007 is a general-purpose semiempirical quantum mechanics package for the study of chemical properties and reactions in gas, solution, or solid-state.
		Quantum is a pure physics based molecular docking software which calculates Kd of a protein-ligand complex, and ligand position in the protein active site.
	www.redbrick.dcu.ie /~noel/linux4chemistry (9822 words)

	MIT OpenCourseWare \| Chemistry \| 5.73 Introductory Quantum Mechanics I, Fall 2005 \| Home
		5.73 covers fundamental concepts of quantum mechanics: wave properties, uncertainty principles, Schrödinger equation, and operator and matrix methods.
		Basic applications of the following are discussed: one-dimensional potentials (harmonic oscillator), three-dimensional centrosymmetric potentials (hydrogen atom), and angular momentum and spin.
		The course also examines approximation methods: variational principle and perturbation theory.
	ocw.mit.edu /OcwWeb/Chemistry/5-73Fall-2005/CourseHome (144 words)

	List of publications (detailed version)
		Popov V. and Sergeev A. Ionization of atoms in weak fields and the asymptotic behavior of higher-order perturbation theory.
		Abstracts of All-Union Conference on the Theory of Atoms and Atomic Spectra.
		Sergeev A. Kvaziklassicheskaia teoriya vozmushcheniy dlia spektroskopicheskih kharakteristik vodorodopodobnyh ionov v plazme (Quasiclassical perturbation theory for spectroscopical characteristics of hydrogen-like atoms in plasma).
	www.asergeev.com /papers/publlong.htm (0 words)

	Historical Notes: History [of quantum theory]
		In 1941 Richard Feynman pointed out that amplitudes in quantum theory could be worked out by using path integrals that sum with appropriate weights contributions from all possible histories of a system.
		But this was not enough, and by the 1930s it was being suggested that the validity of quantum mechanics might be a sign that whole new general frameworks for philosophy or logic were needed - a notion supported by the apparent need to bring consciousness into discussions about measurement in quantum mechanics (see page 1067).
		The peculiar character of quantum mechanics was again emphasized by the idealized experiment of Albert Einstein, Boris Podolsky and Nathan Rosen in 1935.
	www.wolframscience.com /reference/notes/1056a (2138 words)

	Quantum Gravity (Stanford Encyclopedia of Philosophy)
		Theories of quantum gravity, on the other hand, are bedeviled by a host of technical and conceptual problems, questions, and issues which make them unsuited to this approach.
		Loop quantum gravity is less plagued by a lack of predictions, and indeed it is often claimed that the discreteness of area and volume are concrete predictions of the theory.
		Rather, their status in string theory is analogous to the status of particles in quantum field theory (Witten, 2001), which is to say that they are relevant descriptions of the fundamental physics only in situations in which there is a background spacetime with appropriate symmetries.
	plato.stanford.edu /entries/quantum-gravity (6062 words)

	More on Quantum Mechanics
		Quantum mechanics predicts at least three classes of phenomena that classical mechanics and classical electrodynamics cannot account for: (i) the quantization (discretization) of certain physical quantities, (ii) wave-particle duality, and (iii) quantum entanglement.
		Another difficulty with quantum mechanics is that the nature of an object isn't known, in the sense that an object's position, or the shape of the spatial distribution of the probability of presence, is only known by the properties (charge for example) and the environment (presence of an electric potential).
		Quantum electrodynamics is a quantum theory of electrons, positrons, and the electromagnetic field, and served as a role model for subsequent quantum field theories.
	www.artilifes.com /quantum-mechanics.htm (3712 words)

	Perturbation theory - Wikipedia, the free encyclopedia
		Perturbation theory has its roots in 17th century celestial mechanics, where the theory of epicycles was used to make small corrections to the predicted paths of planets.
		Perturbation theory saw a particularly dramatic expansion and evolution with the arrival of quantum mechanics.
		Although perturbation theory was used in the semi-classical theory of the Bohr atom, the calculations were monstrously complicated, and subject to somewhat ambiguous interpretation.
	en.wikipedia.org /wiki/Perturbation_theory (2288 words)

	Quantum field theory Summary
		Quantum field theory originated in the problem of computing the energy radiated by an atom when it dropped from one quantum state to another of lower energy.
		For example, in every quantum theory the global phase of the wave function is arbitrary and does not represent something physical, so the theory is invariant under a global change of phases (adding a constant to the phase of all wave functions, everywhere); this is a global symmetry.
		Quantum field theory was created by Dirac when he attempted to quantize the electromagnetic field in the late 1920s.
	www.bookrags.com /Quantum_field_theory (5286 words)

	String Theory - ApologeticsWiki
		String theory was originally developed and explored during the late 1960s and early 1970s, to explain some peculiarities of the behavior of hadrons (subatomic particles such as the proton and neutron which experience the strong nuclear force).
		Recently, the discovery of the string theory landscape, which suggests that string theory has an exponentially large number of different vacua, led to discussions of what string theory might eventually be expected to predict, and to the worry that the answer might continue to be nothing.
		By applying the ideas of quantum mechanics to strings it is possible to deduce the different vibrational modes of strings, and that each vibrational state appears to be a different particle.
	www.apologeticswiki.com /index.php?title=String_Theory (2722 words)

	Quantum chromodynamics Summary
		Quantum Chromodynamics, or QCD, is the theory describing the strong interactions between quarks and gluons.
		Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction, a fundamental force describing the interactions of the quarks and gluons found in nucleons (such as the proton and the neutron).
		The three kinds of charge in QCD (as opposed to one in Quantum electrodynamics or QED) are usually referred to as "color charge" by loose analogy to the three kinds of color (red, green and blue) perceived by humans.
	www.bookrags.com /Quantum_chromodynamics (2967 words)

	Quantum Gravity
		There are, however, a number of theories of gravitation that involve "gravitons" as the intermediaries between objects but no theory has the precision of a quantum theory of gravitation to explain the effect of gravity.
		The need for a QED emerged from the problem of the interaction of light and matter: Maxwell's theory of electromagnetism had to be changed to be in accord with the new principles of quantum mechanics that had then been developed and was a tremendous success in explaining all of chemistry and properties of substances.
		The need for a quantum theory for gravitation is less justified because we have no reasonable dynamic theory for gravitation and only a handful of experiments and observations to proceed with.
	www.coolissues.com /gravitation/QuantumGravity/qgrav.htm (1840 words)

	No Title
		Their goal is to prevent students, in their rush to take notes on every detail of the lectures, from losing sight of the broader picture: how topics fit together, what examples or particular topics show, and the motivations and justifications for steps taken in class.
		Since this course concerns relativistic quantum theory, we will choose units most suited for such problems: that is, units that eliminate the conversion constants that always crop up in problems involving quantum mechanics and relativity.
		This formalizes relationships you recall from quantum mechanics: a particle's mass is inversely related to its deBroglie (also called Compton) wavelength; and an energy gap between states is inversely related to the lifetime of the higher energy state.
	www.emory.edu /PHYSICS/Faculty/Benson/380-96/notes/1/1.html (783 words)

	439-451
		The relations are discussed among a number of different formulations of perturbation theory for an effective Hamiltonian of a general quantum system.
		Although the definitions and the formulations are apparently different, it is shown that the effective Hamiltonians, which have appeared in the history of time-independent approaches, can be written simply in a unified form.
		P. Löwdin, Perturbation Theory and Its Application to Quantum Mechanics, ed.
	ptp.ipap.jp /link?PTP/70/439 (210 words)

	[hep-th/0510160] Adaptive Perturbation Theory: Quantum Mechanics and Field Theory
		Abstract: Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods.
		The novel feature of adaptive perturbation theory is that it decomposes a given Hamiltonian, $H$, into an unperturbed part and a perturbation in a way which extracts the leading non-perturbative behavior of the problem exactly.
		In this talk I will introduce the method in the context of the pure anharmonic oscillator and then apply it to the case of tunneling between symmetric minima.
	arxiv.org /abs/hep-th/0510160 (220 words)

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