Related papers: Wave function representation of probability distri…

Using a relation between a bi-orthogonal set of equiseparable bases and the weak values of the density matrix we derive an explicit formula for its tomographic reconstruction completely analogous to the standard mutually unbiased bases…

The degree-of-presence (of the quantum system) concept, accompanying that of the wavefunction-reality postulate, is introduced and studied in two ways. To begin with, an incomplete exposition of the present author's views is given.…

A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different…

The probabilistic prediction of quantum theory is mystery. I solved the mystery by a geometrical interpretation of a wave function. This suggests the unification between quantum theory and the theory of relativity. This suggests Many-Worlds…

We analyse the Gaussian wave packet transform. Based on the Fourier inversion formula and a partition of unity, which is formed by a collection of Gaussian basis functions, a new representation of square-integrable functions is presented.…

The quasidistributions corresponding to the diagonal representation of quantum states are discussed within the framework of operator-symbol construction. The tomographic-probability distribution describing the quantum state in the…

Schroedinger's wave function shows many aspects of a state of incomplete knowledge or information ("bit"): (1) it is usually defined on a space of classical configurations, (2) its generic entanglement is, therefore, analogous to…

This paper gives an introduction to the theory of orthogonal projection of functions or signals. Several kinds of decomposition are explored: Fourier, Fourier-Legendre, Fourier-Bessel series for 1D signals, and Spherical Harmonic series for…

Central to quantum theory, the wavefunction is the complex distribution used to completely describe a quantum system. Despite its fundamental role, it is typically introduced as an abstract element of the theory with no explicit definition.…

Expression for probability distribution is got taking into account a presence and removal of degeneracy on the microstates. Its application allows to describe the process of melting of solids, as saltatory phase transition of the first kind…

We describe a method to perform functional operations on probability distributions of random variables. The method uses reproducing kernel Hilbert space representations of probability distributions, and it is applicable to all operations…

One and two photon wave functions are derived by projecting the quantum state vector onto simultaneous eigenvectors of the number operator and a recently constructed photon position operator [Phys. Rev A 59, 954 (1999)] that couples spin…

Stochastic realization of the wave function in quantum mechanics, with the inclusion of soliton representation of extended particles, is discussed. The concept of Stochastic Qubits is used for quantum computing modeling.

We find a novel phenomenon in the solution to the Wheeler-DeWitt equation by solving numerically the equation assuming $O(4)$-symmetry and imposing the Hartle-Hawking wave function as a boundary condition. In the slow-roll limit, as…

Tomographic probability representation is introduced for fermion fields. The states of the fermions are mapped onto probability distribution of discrete random variables (spin projections). The operators acting on the fermion states are…

The lack of the Max Born interpretation of the wave function as a probability density describing the localization of a quantum system in configuration space is pointed out related to the recent category based model of quantum mechanics…

Bayes spaces were initially designed to provide a geometric framework for the modeling and analysis of distributional data. It has recently come to light that this methodology can be exploited to provide an orthogonal decomposition of…

Wavelet estimators for a probability density f enjoy many good properties, however they are not "shape-preserving" in the sense that the final estimate may not be non-negative or integrate to unity. A solution to negativity issues may be to…

We introduce an algorithm of joint approximation of a function and its first derivative by alternative orthogonal polynomials on the interval [0,1].The algorithm exhibits properties of shape preserving approximation for the function. A weak…

The operational calculus associated with special polynomials has proven to be a powerful tool for analyzing and simplifying their properties. This article examines the bivariate degenerate Hermite polynomials with a focus on their…