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... Clearly, this has zeros when x1 = 0, L, when x2 = 0, L, and when x1 = x2 . If the particles were charged, they would repel each other through the Coulomb interaction. Therefore, in the spin 1/2 case, the triplet state would have the lower energy, because the particles tend to be further apart. This ...
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... localization.12 Periodic orbits and their bifurcations also form the basis of Kellman’s approach to the analysis of resonantly coupled modes, in which a systematic study is made of bifurcations on the polyad phase sphere.10 A key to the more systematic application of po theory to vibrational spectra ...
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... But they could be solved if a classical Satisfiability or one of other similar Decision Functions were solvable. This can be done using Grover Algorithm. This chapter will present quantum algorithms: Deutsch, Deutsch-Jozsa, BernsteinVazirani and their modifications and next the Grover algorithm. Nex ...
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... two principles, both more philosophical than scientific. First, local fields were not directly measurable. Thus they were unphysical and meaningless. Instead, one should formulate the theory using the observable S-Matrix elements measured in scattering experiments. Microscopic dynamics was renounced ...
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... basis states. Each basis state corresponds to a pattern of N parentheses and dots, such as () • (())•. The parentheses must obey the typographical rules for nesting, and the dots must not be inside any of the parentheses. These rules imply that the () pairs consist of one even and one odd site, and ...
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... Abstract. The approach to equilibrium of a nondegenerate quantum system involves the damping of microscopic population oscillations, and, additionally, the bringing about of detailed balance, i.e. the achievement of the correct Boltzmann factors relating the populations. These two are separate effect ...
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... This can be proved by showing all the minimizing geodesies are short. A general reference is Milnor's book on Morse theory [Mi]. The infinite dimensional loop spaces Q(M) were originally handled by retraction onto finite dimensional spaces using piecewise solutions as approximations. This does not w ...
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introduction to the electron theory of metals - Assets

... need for constructing a theory compatible with the dual nature of radiation having both wave and particle properties. In 1925, Pauli [6] postulated a simple sorting-out principle by thoroughly studying a vast amount of spectroscopic data including those associated with the Zeeman effect described be ...
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Hidden variable theory

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