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continuous spectrum | A Wisdom Archive on continuous spectrum | | continuous spectrum A selection of articles related to continuous spectrum | |
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| ARTICLES RELATED TO continuous spectrum | |
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| | |  continuous spectrum: Encyclopedia II - Computational chemistry - Ab initio methodsThe programs used in computational chemistry are based on many different quantum-chemical methods that solve the molecular Schrödinger equation associated with the molecular Hamiltonian. Methods that do not include empirical or semi-empirical parameters in their equations - are derived directly from theoretical principles, with no inclusion of experimental data - are generally called ab initio methods. Most of the time this is referring to approximate quantum mechanical calculations. The approximations made in these cases, however, a ...
See also:Computational chemistry, Computational chemistry - Introduction, Computational chemistry - Ab initio methods, Computational chemistry - Electronic structure, Computational chemistry - Chemical dynamics, Computational chemistry - Semiempirical methods, Computational chemistry - Electronic structure, Computational chemistry - Molecular mechanics, Computational chemistry - Software packages Read more here: » Computational chemistry: Encyclopedia II - Computational chemistry - Ab initio methods |
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| | | | continuous spectrum: Encyclopedia II - Energy level - Intrinsic energy levels
Energy level - Orbital state energy level.
Assume an electron in a given atomic orbital. The energy of its state is mainly determined by the electrostatic interaction of the (negative) electron with the (positive) nucleus, calculatable using the principal quantum number . The energy levels of an electron around a nucleus with charge are given by
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where is the Rydberg constant. The typical magnitude is from 1 eV to 103 eV. The Rydb ...
See also:Energy level, Energy level - Intrinsic energy levels, Energy level - Orbital state energy level, Energy level - Fine structure splitting, Energy level - Hyperfine structure, Energy level - Electrostatic interaction of an electron with other electrons, Energy level - Energy levels due to external fields, Energy level - Zeeman effect, Energy level - Zeeman effect taking spin into account, Energy level - Stark effect, Energy level - Paschen-Back effect Read more here: » Energy level: Encyclopedia II - Energy level - Intrinsic energy levels |
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| | | | continuous spectrum: Encyclopedia II - Computational chemistry - Introduction The term theoretical chemistry may be defined as a mathematical description of chemistry, whereas computational chemistry is usually used when a mathematical method is sufficiently well developed that it can be automated for implementation on a computer. Note that the words exact and perfect do not appear here, as very few aspects of chemistry can be computed exactly. Almost every aspect of chemistry, however, can be and has been described in a quali ...
See also:Computational chemistry, Computational chemistry - Introduction, Computational chemistry - Ab initio methods, Computational chemistry - Electronic structure, Computational chemistry - Chemical dynamics, Computational chemistry - Semiempirical methods, Computational chemistry - Electronic structure, Computational chemistry - Molecular mechanics, Computational chemistry - Software packages Read more here: » Computational chemistry: Encyclopedia II - Computational chemistry - Introduction |
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| | | | continuous spectrum: Encyclopedia II - Sodium vapor lamp - Light pollution considerations For placements where light pollution is of prime importance (for example an observatory parking lot), low pressure sodium is preferred. As it emits light on only one wavelength, it is the easiest to filter out.
One consequence of widespread public lighting is that on cloudy nights, cities with enough public lighting are illuminated by light reflected off the clouds. As sodium vapor lights are often the source of urban illumination, this turns the sky a tinge of orange. If the sky is clear or hazy, the light will radiate over large distances, causing large enough cities to ...
See also:Sodium vapor lamp, Sodium vapor lamp - Low pressure / LPS / SOX, Sodium vapor lamp - High pressure / HPS, Sodium vapor lamp - Theory of operation, Sodium vapor lamp - Light pollution considerations Read more here: » Sodium vapor lamp: Encyclopedia II - Sodium vapor lamp - Light pollution considerations |
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| | | | continuous spectrum: Encyclopedia II - Langlands program - Ideas leading up to the Langlands program In a very broad context, the program built on existing ideas: the philosophy of cusp forms formulated a few years earlier by Israel Gelfand, the work and approach of Harish-Chandra on semisimple Lie groups, and in technical terms the trace formula of Selberg and others.
What initially was very new in Langlands' work, besides technical depth, was the proposed direct connection to number theory, together with t ...
See also:Langlands program, Langlands program - Connection with number theory, Langlands program - The setting of automorphic representations, Langlands program - A general principle of functoriality, Langlands program - Ideas leading up to the Langlands program, Langlands program - Prizes Read more here: » Langlands program: Encyclopedia II - Langlands program - Ideas leading up to the Langlands program |
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| | | | continuous spectrum: Encyclopedia II - Langlands program - A general principle of functoriality Langlands then generalized things further: instead of using the general linear group GLn, other connected reductive groups can be used. Furthermore, given such a group G, Langlands constructs a complex Lie group LG, and then, for every automorphic cuspidal representation of G and every finite-dimensional representation of LG, he defines an L-function. One of his conjectures states that these L-functions satisfy a ...
See also:Langlands program, Langlands program - Connection with number theory, Langlands program - The setting of automorphic representations, Langlands program - A general principle of functoriality, Langlands program - Ideas leading up to the Langlands program, Langlands program - Prizes Read more here: » Langlands program: Encyclopedia II - Langlands program - A general principle of functoriality |
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| | | | continuous spectrum: Encyclopedia II - Computational chemistry - Molecular mechanics In many cases, large molecular systems can be modelled succesfully avoiding quantum mechanical calculations entirely. Molecular mechanics simulations, for example, use a single classical expression for the energy of a compound, for instance the harmonic oscillator. All constants appearing in the equations must be obtained beforehand from experimental data or ab initio calculations.
The database of compounds used for parameterization - (the resulting set of parameters and functions is called the force field) - is crucial to the success ...
See also:Computational chemistry, Computational chemistry - Introduction, Computational chemistry - Ab initio methods, Computational chemistry - Electronic structure, Computational chemistry - Chemical dynamics, Computational chemistry - Semiempirical methods, Computational chemistry - Electronic structure, Computational chemistry - Molecular mechanics, Computational chemistry - Software packages Read more here: » Computational chemistry: Encyclopedia II - Computational chemistry - Molecular mechanics |
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| | | | continuous spectrum: Encyclopedia II - Computational chemistry - Semiempirical methods
Computational chemistry - Electronic structure.
Within the framework of Hartree-Fock calculations, some pieces of information (such as two-elecron integrals) are sometimes approximated or completely omitted. In order to correct for this loss, semiempirical methods are parametrized, that is their results are fitted by a set of parameters, normally in such a way as to produce results that best agree with ...
See also:Computational chemistry, Computational chemistry - Introduction, Computational chemistry - Ab initio methods, Computational chemistry - Electronic structure, Computational chemistry - Chemical dynamics, Computational chemistry - Semiempirical methods, Computational chemistry - Electronic structure, Computational chemistry - Molecular mechanics, Computational chemistry - Software packages Read more here: » Computational chemistry: Encyclopedia II - Computational chemistry - Semiempirical methods |
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| | | | continuous spectrum: Encyclopedia II - Mercury-vapor lamp - Operation When the lamp is first turned on, it will produce a dark blue glow because only a small amount of the mercury is ionized and the gas pressure in the arc tube is very low (so much of the light is produced in the ultraviolet mercury bands). As the main arc strikes and the gas heats up and increases in pressure, the light shifts into the visible range and the high gas pressure causes the mercury emission bands to broaden somewhat, producing a light that appears more-white to the human eye (although it is still not a continuous spectrum). Even at full intensity, the light from a mercury vapor lamp ...
See also:Mercury-vapor lamp, Mercury-vapor lamp - Theory and relations, Mercury-vapor lamp - Variation: Metal halide, Mercury-vapor lamp - Operation, Mercury-vapor lamp - Color considerations, Mercury-vapor lamp - Light pollution considerations, Mercury-vapor lamp - Ultraviolet hazards Read more here: » Mercury-vapor lamp: Encyclopedia II - Mercury-vapor lamp - Operation |
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| | | | continuous spectrum: Encyclopedia II - Mixing mathematics - Topological mixing A form of mixing may be defined without appeal to a measure, making use only of the topology of the system. A system is said to be topologically mixing if, for all non-empty open sets A and B, there exists a value R, such that, for all n > R, one has
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For a continuous-time system, T − n is replaced by Tg, with g the continuous parameter, with the ...
See also:Mixing mathematics, Mixing mathematics - Mixing in stochastic processes, Mixing mathematics - Mixing in dynamical systems, Mixing mathematics - Topological mixing, Mixing mathematics - Generalizations Read more here: » Mixing mathematics: Encyclopedia II - Mixing mathematics - Topological mixing |
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