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.

However, in quantum physics, there is another type of angular momentum, called spin angular momentum, represented by the spin operator S. Almost all elementary particles have spin.

However, this work has been subject to much criticism by quantum chemists as it was concluded that the predicted I < sub > h </ sub > symmetric structure was vibrationally unstable and the resulting cage undergoes a spontaneous symmetry break, yielding a puckered cage with rare T < sub > h </ sub > symmetry ( symmetry of a volleyball ).

However, most chemists followed Kekulé's lead in pursuing and developing what some have called " classical " structure theory, which was modified after the discovery of electrons ( 1897 ) and the development of quantum mechanics ( in the 1920s ).

However, unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity.

However, according to quantum physics, individual molecules ( and atoms, electrons, protons etc.

However, the reason for this correction to the partition function remained obscure until the discovery of quantum mechanics.

However, quantum mechanical effects force electrons to take on discrete positions in orbitals.

However in the case of the free electron laser, atomic energy levels are not involved ; it appears that the operation of this rather exotic device can be explained without reference to quantum mechanics.

However, results from quantum mechanical research have suggested that this configuration is incorrect, and is in fact 7s < sup > 2 </ sup > 5f < sup > 14 </ sup > 7p < sup > 1 </ sup >.

However, in quantum physics, organic chemistry, and biochemistry, the term molecule is often used less strictly, also being applied to polyatomic ions.

However, for macroscopic processes classical mechanics is able to solve problems which are unmanageably difficult in quantum mechanics and hence remains useful and well used.

However, it fails to account for one of the main differences between quantum mechanics and classical mechanics, that is, the effects of measurement.

However, practical problems have prevented one-time pads from being widely used, except with quantum key distribution.

However, when the well becomes very narrow ( on the scale of a few nanometers ), quantum effects become important.

However, the use of canonical quantization has left its mark on the language and interpretation of quantum field theory.

However, it leads to a fairly simple picture of the vacuum state and is not easily amenable to use in some quantum field theories, such as quantum chromodynamics which is known to have a complicated vacuum characterized by many different condensates.

However, in 1905 Albert Einstein interpreted Planck's quantum hypothesis realistically and used it to explain the photoelectric effect, in which shining light on certain materials can eject electrons from the material.

However, quantum mechanics does not pinpoint the exact values of a particle's position and momentum ( since they are conjugate pairs ) or its energy and time ( since they too are conjugate pairs ); rather, it only provides a range of probabilities of where that particle might be given its momentum and momentum probability.

However, the formulation of a complete theory of quantum gravity is hindered by apparent incompatibilities between general relativity ( the most accurate theory of gravity currently known ) and some of the fundamental assumptions of quantum theory.

However, chaotic systems do not have good quantum numbers, and quantum chaos studies the relationship between classical and quantum descriptions in these systems.

However, as a field measurement, it is open to question.

However, in the Coulomb field of a nucleus the translational invariance is broken and single-photon annihilation may occur.

However, for quasi-equilibrium systems ( e. g. spins out of equilibrium with the electromagnetic field ) this argument does not apply, and negative effective temperatures are attainable.

However, it is more common in the field of conservation today that the training required to become a practicing conservator comes from a recognized university course in conservation.

However, it was the identification of vitamins A, C, and E as antioxidants that revolutionized the field and led to the realization of the importance of antioxidants in the biochemistry of living organisms.

However, the recent advent of sabermetrics has created statistics drawing from a greater breadth of player performance measures and playing field variables.

However, Merkle, instead of advancing to second base, ran toward the clubhouse to avoid the spectators mobbing the field, which at that time was a common, acceptable practice.

However, Kusche's research showed that the unclassified version of the Air Force investigation report stated that the debris field defining the second " crash site " was examined by a search and rescue ship, and found to be a mass of seaweed and driftwood tangled in an old buoy.

However, Ogden prescribed that any student should learn an additional 150-word list for everyday work in some particular field, by adding a word list of 100 words particularly useful in a general field ( e. g., science, verse, business, etc.

However, other professionals that play a more peripheral role in the field of professional sports ( e. g. coaches, general managers, referees, commentators and announcers, sports team owners and executives, sports commissioners ) who are more active in the internal aspects of field tend to remain in obscurity and are less likely to achieve celebrity status.

However, the sibling field of cognitive neuroscience has provided evidence of physiological brain states that directly correlate with mental states-thus providing support for the central assumption of cognitive psychology.

However, once the applied electric field approaches the breakdown value, free electrons become sufficiently accelerated by the electric field to create additional free electrons by colliding, and ionizing, neutral gas atoms or molecules in a process called avalanche breakdown.

However, metal electrode surfaces can cause a region of the vacuum to become conductive by injecting free electrons or ions through either field electron emission or thermionic emission.

However, it remains a commonly used unit for energies in the field of chemistry, and in many countries it remains in common use as a unit of food energy.

However, an errant throw by Tulowitzki sailed past Clint Barmes and into right field, scoring another run and putting runners at 1st and 3rd.

However, whether this is possible depends on how the field of complex numbers is derived in the first place: it may not be possible to distinguish a complex number from its conjugate ( say, 3 + i from 3-i ), since it is impossible to find a property of one that is not also a property of the other, without falling back on the underlying set-theoretic definition.

However, Delphinus is in a rich Milky Way star field.

However, Fahrenheit's interest in natural science led him to begin studies and experimentation in that field.

* However, if we think of as the field of real numbers, then the direct product does not exist-naively defining in a similar manner to the above examples would not result in a field since the element does not have a multiplicative inverse.

However, charges and currents produce EMR only indirectly — rather, in EMR, both the magnetic and electric fields are produced by changes in the other type of field, not directly by charges and currents.

However, in the far-field EM radiation which is described by the two source-free Maxwell curl operator equations, a more correct description is that a time-change in one type of field is proportional to a space-change in the other.