Quantum Basics

Jean Bricmont

Ted Hurley

A unitary matrix is shown to be a product of certain {\em basic} unitary matrices and the product is unique up to order. A basic unitary matrix itself is a product of {\em minimal basic} matrices. A unitary $n\times n$ matrix can be expressed as a product of at most $n$ basic matrices. A basic matrix is defined in terms of an idempotent matrix; the idempotent matrix used in the definition of a minimal basic unitary matrix is a {\em density} matrix. This gives builders for unitary matrices. Quantum logic gates are represented by unitary matrices thus giving unique building material for quantum logic gates.

Prabir Kanti Basu, Hrishikesh Dhasmana

Daniele Di Nunzio

This article tries to propose an analysis of the photons and wave-particles in terms of rhythmic cycles, considering their dynamics and geometry. In the theoretical hypothesis of the Rhythmic Quantum Mechanics, the photon has a basic quantum cycle, and each wave-particle has its cycle related to the basic quantum cycle of the photon by a quantum rhythmic ratio. Electromagnetic fields and massive wave-particles follow the same universal rhythmic space-time dynamics of the basic quantum cycle. The article presents the relations between the basic quantum cycle of the photon, the wave-particles at rest and in relativistic motion, considering the Planck, Compton and de Broglie scale of energy, momentum, frequency, velocity, mass, time, wavelength. Introduction This article tries to analyse the relation between the basic quantum cycle of the photon and the wave-particles.In the theoretical hypothesis of the Rhythmic Quantum Mechanics, the photon has a universal basic quantum cycle, and each wave-particle has its cycles related to the basic quantum cycle of the photon by the quantum rhythmic ratio (Rq).The cycle of each wave-particle emerges from a rhythmic relationship with the basic quantum cycle. RQM tries to describe the physical reality analysing fundamental fields and wave-particles in terms of rhythmic cycles, considering their dynamics and geometry.Wave-particles follow a universal dynamic (a rhythmic ratio related to the basic quantum cycle of the photon). The distinction of the wave-particles is determined by the scale relationship with the basic quantum cycle of the photon (rhythmic hierarchy). Light and matter follow the same universal space-time dynamics. In fundamental physics, the relations of quantities across classical, relativistic, and ultrarelativistic regimes are directly related to the Lorentz factor. In coherence with the fundamental physics, RQM tries to offer a global and unified interpretation of these relations, through a single dynamical space-time parameter, the relativistic rhythmic ratio, and a universal dynamic related to the basic quantum cycle of the photon.

yeonseo

V. Grecchi

This paper is a continuation of the previous one: "Quantum mechanics: some basic techniques for some basic models, I: The models".The main subject is the perturbation theory in quantum mechanics giving diverging perturbation series for the energy levels of the oscillators.Thus, a short historical introduction on the methods of the sum of diverging power series is given.