pdf - at www.arxiv.org.
... gases could be described with the use of three conceptually different kinds of entropy. They are the thermodynamic entropy à la Clausius, the kinetic entropy that describes the gas’ relaxation to thermodynamic equilibrium, and a statistical entropy that is expected to be the logarithm of the number ...
... gases could be described with the use of three conceptually different kinds of entropy. They are the thermodynamic entropy à la Clausius, the kinetic entropy that describes the gas’ relaxation to thermodynamic equilibrium, and a statistical entropy that is expected to be the logarithm of the number ...
Dynamical Theories of Brownian Motion
... the audience is irrelevant. Physicists lost interest in the phenomenon of Brownian motion about thirty or forty years ago. If a modern physicist is interested in Brownian motion, it is because the mathematical theory of Brownian motion has proved useful as a tool in the study of some models of quant ...
... the audience is irrelevant. Physicists lost interest in the phenomenon of Brownian motion about thirty or forty years ago. If a modern physicist is interested in Brownian motion, it is because the mathematical theory of Brownian motion has proved useful as a tool in the study of some models of quant ...
Quantum networks in the presence of D B
... We now concentrate on a periodic tiling with the hexagonal symmetry, called T3 (Fig 5a). This is a periodic hexagonal structure with three sites per a unit cell, one sixfold coordinated and two threefold coordinated. It is also an example of a twodimensional regular bipartite lattice containing node ...
... We now concentrate on a periodic tiling with the hexagonal symmetry, called T3 (Fig 5a). This is a periodic hexagonal structure with three sites per a unit cell, one sixfold coordinated and two threefold coordinated. It is also an example of a twodimensional regular bipartite lattice containing node ...
Interpreting Quantum Mechanics in Terms of - Philsci
... problem. To begin with, we argue that the two no-collapse quantum theories, namely the de Broglie-Bohm theory and the many-worlds interpretation, are inconsistent with protective measurement and the picture of random discontinuous motion of particles. This result strongly suggests that wavefunction ...
... problem. To begin with, we argue that the two no-collapse quantum theories, namely the de Broglie-Bohm theory and the many-worlds interpretation, are inconsistent with protective measurement and the picture of random discontinuous motion of particles. This result strongly suggests that wavefunction ...
Slajd 1
... which the propagating neutrino is described by a wave packet state determined by the production process C.Giunti JHEP 0211(2002)017 ...
... which the propagating neutrino is described by a wave packet state determined by the production process C.Giunti JHEP 0211(2002)017 ...
NON-HERMITIAN QUANTUM MECHANICS by KATHERINE JONES
... there any real reason to pursue non-Hermitian quantum mechanics? In what follows I hope to convince you that there is, and that non-Hermitian quantum mechanics is the idea that one might discover new and physically relevant theories by considering other inner products than the standard one. We begin ...
... there any real reason to pursue non-Hermitian quantum mechanics? In what follows I hope to convince you that there is, and that non-Hermitian quantum mechanics is the idea that one might discover new and physically relevant theories by considering other inner products than the standard one. We begin ...
Hydrogen Atom.
... Applications of group theory in physics start with two very important princples. These are Galileo’s Principle of Relativity (of observers) and Einstein’s Principle of Equivalence (of states). We show how these principles are used to establish the standard framework for the application of geometric ...
... Applications of group theory in physics start with two very important princples. These are Galileo’s Principle of Relativity (of observers) and Einstein’s Principle of Equivalence (of states). We show how these principles are used to establish the standard framework for the application of geometric ...
ECE2 The Second Paradigm Shift Chapter Five
... In UFT333 it is shown that the ECE2 hamiltonian can be quantized using at least four different classification schemes, each leading to different spectral results. The method used by Dirac is a subjective choice of approximation. The schemes in UFT333 are illustrated with rigorous quantization of the ...
... In UFT333 it is shown that the ECE2 hamiltonian can be quantized using at least four different classification schemes, each leading to different spectral results. The method used by Dirac is a subjective choice of approximation. The schemes in UFT333 are illustrated with rigorous quantization of the ...
Matematiska institutionen Department of Mathematics Covering the sphere with noncontextuality inequalities
... instead of spin 1/2 particles. In this sense Bell’s theorem is much simpler. For all the details see the original paper Kochen and Specker [1968]. Interestingly enough, this paper was published before the CHSH paper, though all details were first understood after they were both published. The theore ...
... instead of spin 1/2 particles. In this sense Bell’s theorem is much simpler. For all the details see the original paper Kochen and Specker [1968]. Interestingly enough, this paper was published before the CHSH paper, though all details were first understood after they were both published. The theore ...
Kinetic Energy Estimates for the Accuracy of the Time
... γΦHF,t kL1 . In the present article we restrict ourselves to the case k = 1. Derivation of the TDHF Equation. The derivation of the TDHF equation may be seen as part of the quest for a derivation of macroscopic, or mesoscopic, dynamics from the microscopic classical or quantum-mechanical dynamics of ...
... γΦHF,t kL1 . In the present article we restrict ourselves to the case k = 1. Derivation of the TDHF Equation. The derivation of the TDHF equation may be seen as part of the quest for a derivation of macroscopic, or mesoscopic, dynamics from the microscopic classical or quantum-mechanical dynamics of ...
Why is there an invariant speed c?
... The wavefunction gives not the density of stuff, but gives rather (on squaring its modulus) the density of probability. Probability of what exactly? Not of the electron being there, but of the electron being found there, if its position is ‘measured’. Why this aversion to ‘being’ and insistence on ‘ ...
... The wavefunction gives not the density of stuff, but gives rather (on squaring its modulus) the density of probability. Probability of what exactly? Not of the electron being there, but of the electron being found there, if its position is ‘measured’. Why this aversion to ‘being’ and insistence on ‘ ...
Wave function
A wave function in quantum mechanics describes the quantum state of an isolated system of one or more particles. There is one wave function containing all the information about the entire system, not a separate wave function for each particle in the system. Its interpretation is that of a probability amplitude. Quantities associated with measurements, such as the average momentum of a particle, can be derived from the wave function. It is a central entity in quantum mechanics and is important in all modern theories, like quantum field theory incorporating quantum mechanics, while its interpretation may differ. The most common symbols for a wave function are the Greek letters ψ or Ψ (lower-case and capital psi).For a given system, once a representation corresponding to a maximal set of commuting observables and a suitable coordinate system is chosen, the wave function is a complex-valued function of the system's degrees of freedom corresponding to the chosen representation and coordinate system, continuous as well as discrete. Such a set of observables, by a postulate of quantum mechanics, are Hermitian linear operators on the space of states representing a set of physical observables, like position, momentum and spin that can, in principle, be simultaneously measured with arbitrary precision. Wave functions can be added together and multiplied by complex numbers to form new wave functions, and hence are elements of a vector space. This is the superposition principle of quantum mechanics. This vector space is endowed with an inner product such that it is a complete metric topological space with respect to the metric induced by the inner product. In this way the set of wave functions for a system form a function space that is a Hilbert space. The inner product is a measure of the overlap between physical states and is used in the foundational probabilistic interpretation of quantum mechanics, the Born rule, relating transition probabilities to inner products. The actual space depends on the system's degrees of freedom (hence on the chosen representation and coordinate system) and the exact form of the Hamiltonian entering the equation governing the dynamical behavior. In the non-relativistic case, disregarding spin, this is the Schrödinger equation.The Schrödinger equation determines the allowed wave functions for the system and how they evolve over time. A wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name ""wave function"", and gives rise to wave–particle duality. The wave of the wave function, however, is not a wave in physical space; it is a wave in an abstract mathematical ""space"", and in this respect it differs fundamentally from water waves or waves on a string.For a given system, the choice of which relevant degrees of freedom to use are not unique, and correspondingly the domain of the wave function is not unique. It may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space, the two are related by a Fourier transform. These descriptions are the most important, but they are not the only possibilities. Just like in classical mechanics, canonical transformations may be used in the description of a quantum system. Some particles, like electrons and photons, have nonzero spin, and the wave function must include this fundamental property as an intrinsic discrete degree of freedom. In general, for a particle with half-integer spin the wave function is a spinor, for a particle with integer spin the wave function is a tensor. Particles with spin zero are called scalar particles, those with spin 1 vector particles, and more generally for higher integer spin, tensor particles. The terminology derives from how the wave functions transform under a rotation of the coordinate system. No elementary particle with spin 3⁄2 or higher is known, except for the hypothesized spin 2 graviton. Other discrete variables can be included, such as isospin. When a system has internal degrees of freedom, the wave function at each point in the continuous degrees of freedom (e.g. a point in space) assigns a complex number for each possible value of the discrete degrees of freedom (e.g. z-component of spin). These values are often displayed in a column matrix (e.g. a 2 × 1 column vector for a non-relativistic electron with spin 1⁄2).In the Copenhagen interpretation, an interpretation of quantum mechanics, the squared modulus of the wave function, |ψ|2, is a real number interpreted as the probability density of measuring a particle as being at a given place at a given time or having a definite momentum, and possibly having definite values for discrete degrees of freedom. The integral of this quantity, over all the system's degrees of freedom, must be 1 in accordance with the probability interpretation, this general requirement a wave function must satisfy is called the normalization condition. Since the wave function is complex valued, only its relative phase and relative magnitude can be measured. Its value does not in isolation tell anything about the magnitudes or directions of measurable observables; one has to apply quantum operators, whose eigenvalues correspond to sets of possible results of measurements, to the wave function ψ and calculate the statistical distributions for measurable quantities.The unit of measurement for ψ depends on the system, and can be found by dimensional analysis of the normalization condition for the system. For one particle in three dimensions, its units are [length]−3/2, because an integral of |ψ|2 over a region of three-dimensional space is a dimensionless probability.