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Many of the results of quantum mechanics are not easily visualized in terms of classical mechanics — for instance, the ground state in a quantum mechanical model is a non-zero energy state that is the lowest permitted energy state of a system, as opposed to a more " traditional " system that is thought of as simply being at rest, with zero kinetic energy.
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Many and results
Many workers believe that the response is proportional to the incident momentum of the particles, a relation deduced from laboratory results linearly extrapolated to meteoritic velocities.
Many anagram servers ( for example, the Internet Anagram Server ) can control the search results, by excluding or including certain words, limiting the number or length of words in each anagram, or limiting the number of results.
Many significant areas of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be stated, and proved, in a much simpler way than without the use of categories.
Many studies of treatments used by chiropractors have been conducted, often with conflicting results.
Many prominent figures testified in that trial, including members of the parliamentary committee investigating the reasons for the defeat, so some of its results were made public long before the publication of the committee report in 1928.
Many results in classical thermodynamics are not easily applied to non-equilibrium systems.
Many results about plane figures are proved, e. g., If a triangle has two equal angles, then the sides subtended by the angles are equal.
Many labels expected New York freestyle and Miami freestyle to have the same audience and thought that the same promotional strategy would work for both genres, which often led to poor results for the New York – based freestyle.
* Compact groups or locally compact groups — Many of the results of finite group representation theory are proved by averaging over the group.
* Lie groups — Many important Lie groups are compact, so the results of compact representation theory apply to them.
Many graduate schools require applicants to take the exam and base admission decisions in part on the results.
Many people believe that the fact that qualified commentators abroad were beginning to doubt the official Spanish version the very same day of the attacks while the government insisted on ETA's implication directly influenced the results of the election.
Many bizarre states of consciousness are actually the results of dissociation of certain mental functions from " I ".
Many of the experimenters have claimed positive results.
Many mercantilists also realized that the inevitable results of quotas and price ceilings were black markets.
Many ways of analytically evaluating the results of this sort of experiment have been developed.
Many in the scientific community consider parapsychology a pseudoscience as they claim it continues to explore the hypothesis that psychic abilities exist despite a century of experimental results that fail to conclusively demonstrate that hypothesis.
Many studies have investigated a genetic link between this variation and cancer susceptibility, however, the results have been controversial.
Many studies seeking to detect, understand, and utilize telepathy have been done, but according to the prevailing view among scientists, telepathy lacks replicable results from well-controlled experiments.
Many bakers see the starter method as a compromise between the highly reliable results of baker's yeast and the flavor and complexity of a longer fermentation.
Many suggest this results in a growing inequality of status between the rich and the poor.
Many nations sent oceanographic observations to Maury at the Naval Observatory, where he and his colleagues evaluated the information and gave the results worldwide distribution.
Many statisticians believe that the mainstream public should be informed of the counter-intuitive results in statistics such as Simpson's paradox.
Many and quantum
Many physicists have subscribed to the instrumentalist interpretation of quantum mechanics, a position often equated with eschewing all interpretation.
Many areas of mathematics and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing.
Many of these structures are drawn from functional analysis, a research area within pure mathematics that was influenced in part by the needs of quantum mechanics.
Many transitions involving electromagnetic radiation are strictly forbidden under quantum mechanics.
* Many macroscopic properties of a classical system are a direct consequence of the quantum behavior of its parts.
Many quantum chemical studies assume the nuclei are at rest ( Born – Oppenheimer approximation ).
Many of the same entropy measures in classical information theory can also be generalized to the quantum case, such as Holevo entropy and the conditional quantum entropy.
Many of the successes of quantum computation and communication, such as quantum teleportation and superdense coding, make use of entanglement, suggesting that entanglement is a resource that is unique to quantum computation.
Many of the accepted notions of a unified theory of physics since the 1970s, including string theory, superstring theory, M-theory, loop quantum gravity, all assume, and to some degree depend upon, the existence of the graviton.
Many foundational contributions to quantum mechanics were made in Weimar Germany or by German scientists during the Weimar period.
Many quantum phase transitions in two-dimensional electron gases belong to this class.
Many of these conceptual problems, however, resolve in the phase-space formulation of quantum mechanics, where the same variables with the same interpretation are utilized to describe both quantum and classical mechanics.
Many of the ab initio quantum chemistry methods use perturbation theory directly or are closely related methods.
Many interesting results in modern computing are closely related to this problem — reversible computing, quantum computing and physical limits to computing, are examples.
Many theories have been proposed since the beginning of quantum mechanics and quantum measurement continues to be an active research area in both theoretical and experimental physics.
Many quantum field theories do violate parity and charge conjugation.
Many different types of regulator are used in quantum field theory calculations, each with its advantages and disadvantages.
Many further results may be obtained, such as Fermi's golden rule, which relates the rate of transitions between quantum states to the density of states at particular energies, and the Dyson series, obtained by applying the iterative method to the time evolution operator, which is one of the starting points for the method of Feynman diagrams.
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