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Ab initio Quantum and ab initio Molecular Dynamics of the
Ab initio Quantum and ab initio Molecular Dynamics of the

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Physics from Computer Science — a position statement —

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... Classical mechanics is a very peculiar branch of physics. It used to be considered the sum total of our theoretical knowledge of the physical universe (Laplace’s daemon, the Newtonian clockwork), but now it is known as an idealization, a toy model if you will. The astounding thing is that probably a ...
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... (i.e. , the existence of negative delays) makes no fundamental difference to the behavior of a network unless there is a closed path for infor mation. Such a path is not necessarily the trajectory of any carrier in the network because bits on different carriers interact and can exchange information ...
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The minimum mass of a charged spherically symmetric object

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Computational Power of the Quantum Turing Automata

... found for which a quantum machine computed the answer with certainty in polynomial time, whereas requiring a probabilistic classical machine to solve the same problem with certainty required exponential time for some inputs. Note, however, that relative to the same oracle, these problems were in BPP ...
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... Postulate 1: A closed system is described by a unit vector in a complex inner product space. Postulate 2: The evolution of a closed system in a fixed time interval is described by a unitary transform. Postulate 3: If we measure the state |ψi of a system in an orthonormal basis |0i · · · |n − 1i, we ...
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... Often these kinds of symmetries are categorized by group theory. Spin conservation comes from the symmetry between spin up and spin down particles. An interaction with one spin up and one spin down particle would be no different if the spins are switched. In group theory it can be represented by the ...
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Particle in a box



In quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example a ball trapped inside a large box, the particle can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow (on the scale of a few nanometers), quantum effects become important. The particle may only occupy certain positive energy levels. Likewise, it can never have zero energy, meaning that the particle can never ""sit still"". Additionally, it is more likely to be found at certain positions than at others, depending on its energy level. The particle may never be detected at certain positions, known as spatial nodes.The particle in a box model provides one of the very few problems in quantum mechanics which can be solved analytically, without approximations. This means that the observable properties of the particle (such as its energy and position) are related to the mass of the particle and the width of the well by simple mathematical expressions. Due to its simplicity, the model allows insight into quantum effects without the need for complicated mathematics. It is one of the first quantum mechanics problems taught in undergraduate physics courses, and it is commonly used as an approximation for more complicated quantum systems.
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