These states are labeled by a set of quantum numbers summarized in the term symbol and usually associated with particular electron configurations, i. e., by occupation schemes of atomic orbitals ( e. g., 1s < sup > 2 </ sup > 2s < sup > 2 </ sup > 2p < sup > 6 </ sup > for the ground state of neon -- term symbol: < sup > 1 </ sup > S < sub > 0 </ sub >).

However, this was the temperature of one particular degree of freedom a quantum property called nuclear spin not the overall average thermodynamic temperature for all possible degrees in freedom.

In particular, these include the laws of quantum mechanics, electromagnetism and statistical mechanics.

In particular, quantum phase transitions refer to transitions where the temperature is set to zero, and the phases of the system refer to distinct ground states of the Hamiltonian.

In particular the application of quantum mechanics to chemistry is called quantum chemistry.

It means that a particular approximation is rigorously defined on first principles ( quantum theory ) and then solved within an error margin that is qualitatively known beforehand.

The energy bands each correspond to a large number of discrete quantum states of the electrons, and most of the states with low energy ( closer to the nucleus ) are occupied, up to a particular band called the valence band.

In particular the application of quantum mechanics to chemistry is called quantum chemistry.

This experimental fact is highly reproducible, and the mathematics of quantum mechanics ( see below ) allows us to predict the exact probability of an electron striking the screen at any particular point.

In 1964, John Bell showed that the predictions of quantum mechanics in the EPR thought experiment are significantly different from the predictions of a particular class of hidden variable theories ( the local hidden variable theories ).

In contrast to bosons, only one fermion can occupy a particular quantum state at any given time.

In a few materials, a much stronger interaction between spins arises because the change in the direction of the spin leads to a change in electrostatic repulsion between neighboring electrons, due to a particular quantum mechanical effect called the exchange interaction.

Gravitons are postulated because of the great success of quantum field theory ( in particular, the Standard Model ) at modeling the behavior of all other known forces of nature as being mediated by elementary particles: electromagnetism by the photon, the strong interaction by the gluons, and the weak interaction by the W and Z bosons.

In scientific research, the behavior of the two fluid phases of helium-4 ( helium I and helium II ), is important to researchers studying quantum mechanics ( in particular the property of superfluidity ) and to those looking at the phenomena, such as superconductivity, that temperatures near absolute zero produce in matter.

In principle all kinds of magnetism originate ( similar to Superconductivity ) from specific quantum-mechanical phenomena ( e. g. Mathematical formulation of quantum mechanics, in particular the chapters on spin and on the Pauli principle ).

Just as he argues that there is no particular reason why particular macroscopic physical features in the brain should give rise to consciousness, he also thinks that there is no particular reason why a particular quantum feature, such as the electromagnetic field in the brain, should give rise to consciousness, either.

The phenomenology of quantum physics arose roughly between 1895 and 1915, and for the 10 to 15 years before the emergence of quantum theory ( around 1925 ) physicists continued to think of quantum theory within the confines of what is now called classical physics, and in particular within the same mathematical structures.

The strongest appeal of the Copernican formulation consisted in just this: ideally, the justification for dealing with special problems in particular ways is completely set out in the basic ' rules ' of the theory.

What with traders trading for so many different objectives, and what with there being so many unique and individualized market theories and trading techniques in use, and more coming into use all the time, it is hard to imagine how any particular theory or technique could acquire enough `` fans '' to invalidate itself.

However, that particular case is a theorem of Zermelo – Fraenkel set theory without the axiom of choice ( ZF ); it is easily proved by mathematical induction.

It is possible to prove many theorems using neither the axiom of choice nor its negation ; such statements will be true in any model of Zermelo – Fraenkel set theory ( ZF ), regardless of the truth or falsity of the axiom of choice in that particular model.

Instead of starting from theory and applying theory to a particular case, casuists start with the particular case itself and then ask what morally significant features ( including both theory and practical considerations ) ought to be considered for that particular case.

Field automorphisms are important to the theory of field extensions, in particular Galois extensions.

Atle Selberg ( 14 June 1917 – 6 August 2007 ) was a Norwegian mathematician known for his work in analytic number theory, and in the theory of automorphic forms, in particular bringing them into relation with spectral theory.

La Longue Marche à travers la théorie de Galois Long March Through Galois Theory is an approximately 1600-page handwritten manuscript produced by Grothendieck during the years 1980 – 1981, containing many of the ideas leading to the Esquisse d ' un programme ( see below, and also a more detailed entry ), and in particular studying the Teichmüller theory.

In the 1990s, Jürgen Schmidhuber described an algorithmic theory of beauty which takes the subjectivity of the observer into account and postulates: among several observations classified as comparable by a given subjective observer, the aesthetically most pleasing one is the one with the shortest description, given the observer ’ s previous knowledge and his particular method for encoding the data.

However, Davy failed to develop a new theory, concluding that " acidity does not depend upon any particular elementary substance, but upon peculiar arrangement of various substances ".

The inability to comprehend any aspect of the thing other than its properties implies, this argument maintains, that one cannot conceive of a bare particular ( a substance without properties ), an implication that directly opposes substance theory.

Chaos theory and the sensitive dependence on initial conditions was described in the literature in a particular case of the three-body problem by Henri Poincaré in 1890.

In particular, Sommerfeld's theory accounted for the Fermi-Dirac statistics satisfied by electrons and was better able to explain the heat capacity and resistivity.

Much of anthropological theory has originated in an appreciation of and interest in the tension between the local ( particular cultures ) and the global ( a universal human nature, or the web of connections between people in distinct places / circumstances ).

Aside from controversies over the merits of particular conspiratorial claims, the general discussion of conspiracy theory is itself a matter of some public contention.

In particular, when a texture is at a steep angle compared to the camera, detail can be lost because the pixel actually takes up a narrow but long trapezoid: in the narrow direction, the pixel is getting information from more texels than it actually covers ( so details are smeared ), and in the long direction the pixel is getting information from fewer texels than it actually covers ( so details fall between pixels ).

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

Evidence is plentiful that early and later also he has been indebted to the Gothic romancers, who deal in extravagant horror, to the symbolists writing at the end of the preceding century, and in particular to the stream-of-consciousness novelists, Henry James and James Joyce among them.

Ptolemy's problem is to forecast where, against the inverted bowl of night, some particular light will be found at future times.

The `` conventional '' image of a particular time and place is not necessarily congruent with the image of the facts as established over the years by scholarly and scientific research.

The symposium provides an opportunity to confront the self with specific statements which were made at particular times by identifiable communicators who were addressing definite audiences -- and throughout several hundred pages everyone is talking about the same key symbol of identification.

But there is one in particular which, it seems to me, deserves special attention.

At Sounion there is a group of beautiful columns, the ruins of a temple to Poseidon, of particular interest at that time, as active reconstruction was in progress.

Each will decide on his own course somewhere between these two extreme cases according to the sense of responsibility which is determined for him by the particular circumstances of his own life.

In Plato's mind there is an irresolvable conflict between the poet and the philosopher, because the poet imitates only particular objects and is incapable of rising to the first level of abstraction, much less the highest level of ideal forms.

The wisdom of granting such tax exemptions is another matter, but this particular instance is, in my opinion, completely satisfactory.

It makes no difference what part of the world is involved, what form of regime, what particular issue.

Molotov, in particular, is being charged with all kinds of sins -- especially with wanting to cut down free public services, to increase rents and fares ; ;

It would seem, then, that movable property and equipment is not taxed as a whole but that certain types are taxed in towns where this is bound to be expedient for that particular kind of personal property.

It is not clear, however, whether they are thinking of all movable property or only of boats, trailers, aircraft or certain other types of personal property whose assessment would be advantageous to their particular towns.

If the resulting difference for the particular State is less or more than these extremes, the State's allotment percentage must be raised or lowered to the appropriate extreme.

Determine if the particular State's unadjusted allotment ( result obtained in item 11 above ) is greater than its maximum allotment, and if so lower its unadjusted allotment to its maximum allotment.

Determine if the particular State's unadjusted allotment ( result obtained in item 11 above ) is less than its minimum ( base ) allotment, and if so raise its unadjusted allotment to its minimum allotment.

If the resulting difference for the particular State is less or more than these extremes, the State's Federal share must be raised or lowered to the appropriate extreme.

For this reason, the more uncertain skywave service was denominated `` secondary '' in our rules, as compared to the steadier, more reliable groundwave `` primary service '', and, for both skywave service and skywave interference, signal strength is expressed in terms of percentage of time a particular signal-intensity level is exceeded -- 50 percent of the time for skywave service, 10 percent of the time for skywave interference.

The exercise I shall discuss in this -- the first of a new series of articles on muscle definition-specialization of a particular body part -- is the One Leg Lunge.