Some Basics

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.

Ricardo A. Broglia, G. Colò, Giovanni Onida +1 more

Tiezheng Qian, Jing-Bo Xu, Xiao-Chun Gao

A new concept of the basic invariants is introduced. With the help of the basic invariants, new high-n squeezed states of the time-dependent harmonic oscillator are constructed. From the basic invariants, the author also finds a general form of invariants which has not been seen thus far in the literature.

O. Costa de Beauregard

Laurens Vanderstraeten

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.