Related papers: Using quantum mechanics for calculation of differe…
Through a new interpretation of Special Theory of Relativity and with a model given for physical space, we can find a way to understand the basic principles of Quantum Mechanics consistently from Classical Theory. It is supposed that…
The main purpose of this article is using the analytic mathods and the quadratic residual transformation technique, and properties of Dedekind sums to study the calculating problem of two kinds hybrid power mean involving the two-term…
Here we make use of the Hellmann-Feynman theorem, with the aim to calculate macroscopic quantum velocities instead of forces, and we show how it is possible to derive the expression of the work per unit time, per unit volume (power density)…
We consider sums of the form $\sum \phi(\gamma)$, where $\phi$ is a given function, and $\gamma$ ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in a given interval. We show how the numerical estimation of such…
This paper studies the exponential of the sum of two non-commuting operators as an infinite product of exponential operators involving repeated commutators of increasing order. It will be shown how to determine two coefficients in front of…
We give two examples where symmetric polynomials play an important role in physics: First, the partition functions of ideal quantum gases are closely related to certain symmetric polynomials, and a part of the corresponding theory has a…
Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the possibility of entanglement between two or more…
During the past decades, quantum mechanical methods have undergone an amazing transition from pioneering investigations of experts into a wide range of practical applications, made by a vast community of researchers. First principles…
The basics of the Wigner formulation of Quantum-Mechanics and few related interpretational issues are presented in a simple language. This formulation has extensive applications in Quantum Optics and in Mixed Quantum-Classical formulations.
We provide a framework for relating certain q-series defined by sums over partitions to multiple zeta values. In particular, we introduce a space of polynomial functions on partitions for which the associated q-series are q-analogues of…
Long sequences of successive direct (projective) measurements or observations of a few "uninteresting" physical quantities of a quantum system may reveal indirect, but precise and unambiguous information on the values of some very…
The wave function in quantum mechanics presents an interesting challenge to our understanding of the physical world. In this paper, I show that the wave function can be understood as four intrinsic relations on physical space. My account…
The double well potential is arguably one of the most important potentials in quantum mechanics, because the solution contains the notion of a state as a linear superposition of `classical' states, a concept which has become very important…
We study two ways of summing an infinite family of noncommutative spectral triples. First, we propose a definition of the integration of spectral triples and give an example using algebras of Toeplitz operators acting on weighted Bergman…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
This book is an attempt to help students transform all of the concepts of quantum mechanics into concrete computer representations, which can be constructed, evaluated, analyzed, and hopefully understood at a deeper level than what is…
We analyze here the energy states and associated wave functions available to a particle acted upon by a delta function potential of arbitrary strength and sign and fixed anywhere within a one-dimensional infinite well. We consider how the…
We introduce and survey results on two families of zeta functions connected to the multiplicative and additive theories of integer partitions. In the case of the multiplicative theory, we provide specialization formulas and results on the…
A $q$-analogue of the Hurwitz zeta-function is introduced through considerations on the spectral zeta-function of quantum group $SU_{q}(2)$, and its analytic aspects are studied via the Euler-MacLaurin summation formula. Asymptotic formulas…
Using a new Bayesian method for solving inverse quantum problems, potentials of quantum systems are reconstructed from coordinate measurements in non-stationary states. The approach is based on two basic inputs: 1. a likelihood model,…