We review the significance and input of operator theory in the field of quantum mechanics. In particular, we survey the world of microwaves. We also explore the applications in electricity and magnetism.
Practical developments in such fields as optical coherence, communication engineering, and laser technology have developed from the applications of stochastic methods. This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory.The text assumes a basic knowledge of fun
The classical or semiclassical theory presented in Chapter 2 gives a satisfactory account of light-matter interactions in some cases. However, a detailed understanding of different processes requires a quantum mechanical theory of radiation. The quantum theory of light, like classical theory, is also based on Maxwell's equations. However, in quantum theory the electric field F and the magnetic field H are treated as operators. This chapter develops the correspondence between the two and outlines the method for converting field vectors F and H into quantum mechanical operators. Topics discussed include wave equation in a rectangular cavity, quantization of the electric field, time-dependent perturbation theory, interaction of an electron with the magnetic field, and second-order perturbation theory. Exercises are provided at the end of the chapter.
Superconducting quantum sensors use flux quantization, the Josephson effect and low-loss microwave circuits to measure magnetic flux, microwave signals and photon flux close to fundamental limits. In this review we follow the field from the Bardeen–Cooper–Schrieffer theory and the discovery of Josephson tunnelling to SQUID magnetometers, microwave kinetic inductance detectors and quantum-limited parametric amplifiers. We explain how dc and rf SQUIDs, superconducting resonators, and Josephson and kinetic-inductance amplifiers work, and we describe one measurement chain that covers them all, with separate excitation, response, amplification, control and readout paths and a fluxlocked-loop variant for SQUIDs. Flux and field noise, noise-equivalent power, added noise, bandwidth and dynamic range are defined and compared using numbers taken directly from the primary literature, together with the conditions under which they were measured. We then survey applications in biomagnetism, astronomical imaging, qubit readout and dark-matter searches, and close with the open problems of scalability, environmental noise and fair benchmarking.