Elementary Electric-Circuit Theory

Revisiting Matrix Theory and Electric Circuit Analysis

Matrix Theory has long been applied to many branches of engineering. However, numerical difficulties have limited access to students, especially at the elementary level. This limitation has partially been removed with the development of canned software and modern scientific calculators which operate matrices. However, the approach with matrices ignores this and still follows traditional ways. T...

Quantum Measurement in Electric Circuit

We study fluctuations of electric current in a quantum resistor and derive a general quantum-mechanical formula for the distribution of transmitted charge. For that we introduce a scheme of current measurement that involves a spin 1/2 coupled to the current so that it precesses at the rate proportional to the current. Our approach allows the study of charge transfer without breaking the circuit...

Elementary Number Theory

Elementary Hilbert Space Theory

A Hilbert Space is an inner product space that is complete. Let H be a Hilbert space and for f, g ∈ H, let 〈f, g〉 be the inner product and ‖f‖ = √ 〈f, f〉. (1.1) We will consider Hilbert spaces over C. Most arguments go through for Hilbert spaces over R, and the arguments are simpler. We assume that the reader is familiar with some of the basic facts about the inner product. Let us prove a few t...

THEORY of ELEMENTARY PARTICLES

The theory of elementary particles permitting to explain their constitution, sizes, bond energy, possible channels of decay, spectrum of weights and other properties is offered.