“Anticoherent” Spin States via the Majorana Representation
... vertices together comprise the vertices of a dodecahedron. (See Fig. 2.) This configuration offers a highly symmetrical way of inscribing five tetrahedra in the sphere. Now, as the tetrahedral perfect states happen to “live” in a space of five dimensions, a question naturally presents itself: Is it ...
... vertices together comprise the vertices of a dodecahedron. (See Fig. 2.) This configuration offers a highly symmetrical way of inscribing five tetrahedra in the sphere. Now, as the tetrahedral perfect states happen to “live” in a space of five dimensions, a question naturally presents itself: Is it ...
Short introduction to quantum mechanics
... the corresponding processes. Just as well of course one could say that physical phenomena are a question of dimensions or of the scale under consideration. Measurements of macroscopical properties are determined by macroscopical dimensions, those of microscopical properties by the dimensions in the ...
... the corresponding processes. Just as well of course one could say that physical phenomena are a question of dimensions or of the scale under consideration. Measurements of macroscopical properties are determined by macroscopical dimensions, those of microscopical properties by the dimensions in the ...
No Slide Title
... For centro-symmetric systems in which the force works in the same direction as r we must have dL dt = 0 : THE ANGULAR MOMENTUM IS CONSERVED ...
... For centro-symmetric systems in which the force works in the same direction as r we must have dL dt = 0 : THE ANGULAR MOMENTUM IS CONSERVED ...
Dissipative decoherence in the Grover algorithm
... hardware [11]. This second type of errors, e.g. static imperfections, gives a more rapid decay of fidelity as it has been shown in [12,10]. In the case of quantum algorithms for a complex dynamic these imperfections lead to the fidelity decrease described by a universal decay law given by the random ...
... hardware [11]. This second type of errors, e.g. static imperfections, gives a more rapid decay of fidelity as it has been shown in [12,10]. In the case of quantum algorithms for a complex dynamic these imperfections lead to the fidelity decrease described by a universal decay law given by the random ...
Transition function for the Toda chain model
... N-th particle coordinate. We apply methods of the paper [DKM] to obtain these eigenfunctions as a product of Λ-operators reproducing the Gauss-Givental formula [GKLO], [Giv]. This form of eigenfunctions of the open Toda chain leads to an integral representation that appeared first in [Giv] employin ...
... N-th particle coordinate. We apply methods of the paper [DKM] to obtain these eigenfunctions as a product of Λ-operators reproducing the Gauss-Givental formula [GKLO], [Giv]. This form of eigenfunctions of the open Toda chain leads to an integral representation that appeared first in [Giv] employin ...
Electron and hole wave functions in self
... shape or composition asymmetry in the vertical 共growth兲 direction. We now turn to the electron and hole wave functions in quantum rings, considering first the role of the piezoelectric potential in rings which are symmetric in the vertical direction. Figures 3共a兲 and 3共b兲 are birds-eye views of the ...
... shape or composition asymmetry in the vertical 共growth兲 direction. We now turn to the electron and hole wave functions in quantum rings, considering first the role of the piezoelectric potential in rings which are symmetric in the vertical direction. Figures 3共a兲 and 3共b兲 are birds-eye views of the ...
QUANTUM MATTERS What is the matter? Einstein`s
... a quantization process. Two basic principles for quantum systems are Unitarity and Locality, i.e., our quantum system’s Hamiltonian is Hermitian and a sum of local terms. Since every physical quantum system is subject to un-controlled perturbations and we want our Hamiltonian to represent a stable p ...
... a quantization process. Two basic principles for quantum systems are Unitarity and Locality, i.e., our quantum system’s Hamiltonian is Hermitian and a sum of local terms. Since every physical quantum system is subject to un-controlled perturbations and we want our Hamiltonian to represent a stable p ...
Pulse-train control of photofragmentation at constant field energy
... between the pulses.36 Each pulse in the two-pulse sequence creates a wave packet and the interference between the two excited wave packets G1 and G2 gives rise to a time-dependent overlap term in the total population, given by 2Re{G1 (t)|G2 (t)}. For nonoverlapping Gaussian pulses with a temporal ...
... between the pulses.36 Each pulse in the two-pulse sequence creates a wave packet and the interference between the two excited wave packets G1 and G2 gives rise to a time-dependent overlap term in the total population, given by 2Re{G1 (t)|G2 (t)}. For nonoverlapping Gaussian pulses with a temporal ...
Limitations on the superposition principle: superselection
... the random spin orientations in the beam—note that such random behaviour has nothing to do with quantum features. To grasp the situation better, let us think of what we should expect of a spin measurement in an unfiltered beam? It is clear that any measurement should produce the classical (i.e. non- ...
... the random spin orientations in the beam—note that such random behaviour has nothing to do with quantum features. To grasp the situation better, let us think of what we should expect of a spin measurement in an unfiltered beam? It is clear that any measurement should produce the classical (i.e. non- ...
Experiments in “Quantum Erasure” and “Delayed
... the same setup only they are more complicated in the ‘Test’ section. They use beam splitters and more crystals to combine paths after the Main screen so that both sets of results are obtained for the same photon. ...
... the same setup only they are more complicated in the ‘Test’ section. They use beam splitters and more crystals to combine paths after the Main screen so that both sets of results are obtained for the same photon. ...
Chaos, Quantum-transactions and Consciousness
... Many particles [bosons] existing in one wave function, illustrated by the laser and superconductors. ...
... Many particles [bosons] existing in one wave function, illustrated by the laser and superconductors. ...
. of Statistica. nterpretation
... to apply only to an ensemble of similarily prepared systems, rather than supposing, as is often done, that it exhaustively represents an individual physical system. Most of the problems associated with the quantum theory of measurement are artifacts of the attempt to maintain the latter interpretati ...
... to apply only to an ensemble of similarily prepared systems, rather than supposing, as is often done, that it exhaustively represents an individual physical system. Most of the problems associated with the quantum theory of measurement are artifacts of the attempt to maintain the latter interpretati ...
implications of quantum logic to the notion of transcendence
... world is the key and essential element to the solution of any conceptual problems of quantum mechanics. The success of mathematical models in exploring reality and in solving conceptual problems of quantum mechanics is a clear indication that logic has its source in the laws of nature. Since logic h ...
... world is the key and essential element to the solution of any conceptual problems of quantum mechanics. The success of mathematical models in exploring reality and in solving conceptual problems of quantum mechanics is a clear indication that logic has its source in the laws of nature. Since logic h ...
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.