Related papers: Quantum mechanical sum rules for two model systems
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates.…
Can any element in a sufficiently large finite field be represented as a sum of two $d$th powers in the field? In this article, we recount some of the history of this problem, touching on cyclotomy, Fermat's last theorem, and diagonal…
In one-dimensional case, it is shown that the basic principles of quantum mechanics are properties of the set of intermediate cardinality.
A simple model is considered to study the effects of finite size and internal structure in the tunneling of bound two-body systems through a potential barrier. It is demonstrated that these effects are able to increase the tunneling…
We examine the quantum mechanical eigensolutions of the two-dimensional infinite well or quantum billiard system consisting of a circular boundary with an infinite barrier or baffle along a radius. Because of the change in boundary…
Non-EQuilibrium (NEQ) statistical physics has not had the same general foundation as that of EQuilibrium (EQ) statistical physics, where forces are derived from potentials such as $1/T = \partial S/\partial U$, and from which other key…
We compare the classical and quantum mechanical position-space probability densities for a particle in an asymmetric infinite well. In an idealized system with a discontinuous step in the middle of the well, the classical and quantum…
A class of sum rules for inelastic light scattering is developed. We show that the first moment of the non-resonant response provides information about the potential energy in strongly correlated systems. The polarization dependence of the…
A recently proposed scheme is used to saturate the spectral side of the QCD sum rules derived from the thermal, two-point correlation functions of the vector and the axial-vector currents. At low temperature, it constructs the spectral…
The status of our understanding of relativistic sum rules is reviewed. The recent development of new theoretical methods for the evaluation of these sum rules offers hope for further advances in this challenging field. These new techniques…
The concept of QCD sum rules is extended to bound states composed of particles with finite mass such as scalar quarks or strange quarks. It turns out that mass corrections become important in this context. The number of relevant corrections…
The theory of quantum thermodynamics investigates how the concepts of heat, work, and temperature can be carried over to the quantum realm, where fluctuations and randomness are fundamentally unavoidable. These lecture notes provide an…
The familiar "modulus squared" form of all quantum mechanical probabilities is derived from an assumption of equal a priori probabilities concerning the final states available.
The gauge invariant operator formulation of the angular momentum sum rule ${1\over2} = J_q + J_g$ for the proton is presented and contrasted with the sum rule for the first moment of the polarised structure function $g_1^p$. The decoupling…
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
In their work [J. Phys. A: Math. Gen. 33, 4427 (2000)], Bender, Brody, and Meister have shown by employing a two-state model of a particle confined in the one-dimensional infinite potential well that it is possible to construct a…
The first law of thermodynamics imposes not just a constraint on the energy-content of systems in extreme quantum regimes, but also symmetry-constraints related to the thermodynamic processing of quantum coherence. We show that this…
A new method of fundamental quantum data sampling on basis of an optimum measuring scale has been designed. The method was applied for minimization of redundant experimental data in different fields of physics. Basing of this method there…
Classical and quantum mechanics laws are rebuilt in the frame of new thermodynamics. Heat is the sum of kinetic energy, system work, and system potential of a system, while force is the heat gradients over distance. Hence, collision,…
We consider two aspects of quantum game theory: the extent to which the quantum solution solves the original classical game, and to what extent the new solution can be obtained in a classical model.