The theory of the interaction of radiation with matter is fundamentally important for describing how modern semiconductor devices generate, detect, and modulate light. These devices, known as optoelectronic devices, are behind today’s technology in diverse areas, including communications, imaging, spectroscopy, sensing, and energy harvesting. They may also become essential components in future quantum technology based on photons. In this chapter we will learn the basic theoretical formalism for describing light–matter interaction phenomena, starting from microscopic processes such as absorption, spontaneous emission, and stimulated emission and ending with the conditions for achieving gain, which is a fundamental requirement for a laser.

The current–voltage characteristics of modern electronic devices consisting of semiconductor heterostructures, such as resonant tunneling diodes, quantum cascade lasers, and tandem solar cells, are determined by the dynamics of electrons propagating through quantum-engineered 1D potential landscapes. In this chapter, we will develop a general formalism with which to describe transmission probabilities for electron waves propagating through arbitrary potentials, which can be used for analyzing electron motion in semiconductor devices. Furthermore, we will extend our formalism to 1D electrons moving in a general spatially periodic potential, based on which we will describe the basic concepts of the band theory of solids. The central theorem in band theory is the Bloch theorem, which we will derive and then use for discussing the dynamics of electrons in crystalline solids (or Bloch electrons).

The field of quantum computing is developing at a rapid pace, and one can expect paradigm-shifting advances in coming years. The goal of this chapter is for the reader to understand fully the language and basic concepts of quantum information science needed to engage in research and development in this very exciting field in the future. We will apply the mathematical machinery we have acquired so far to develop the quantum counterparts to the classical notions of bits, logic gates, circuits, and algorithms. We will also review some of the promising examples of quantum hardware for physically realizing quantum information processing.

A regrettable amount of mathematical machinery goes into a good understanding of quantum mechanics. This could be avoided if a good intuitive understanding of many quantum systems was possible, but as intuition is generally derived from daily experience (which is governed by classical laws), we cannot expect this to be the case in general. Here, we present an in-depth introduction to the mathematical foundations of quantum mechanics, accompanied, wherever appropriate, by detailed explanations of relevant quantum concepts such as superposition, wavefunction collapse, and the uncertainty principle. As an additional benefit, the language developed in this chapter will be especially useful for describing quantum information science in .

We solve the quantum mechanical harmonic oscillator problem using an operator approach. We define the lowering and raising operators. We use the quantum mechanical harmonic oscillator to review the fundamental ideas of quantum mechanics.We study some examples of time dependence in the harmonic oscillator including the coherent state. We apply the quantum mechanical harmonic oscillator to the study of the vibrations of the nuclei of molecules.

This chapter and Chapter 5 together form an introduction to the Schrödinger equation in one dimension.

Through the Stern-Gerlach experiment, we demonstrate several key concepts about quantum mechanics: quantum mechanics is probabilistic; spin measurements are quantized; quantum measurements disturb the system. We show how to describe the state of a quantum mechanical system mathematically using a ket, which represents all the information we can know about that state.

We learn about unbound states and find that the energies are no longer quantized. We learn about momentum eigenstates and superposing momentum eigenstates in a wave packet. We apply unbound states to the problem of scattering from potential wells and barriers in one dimension.

Following Chadwick’s discovery of the neutron in 1932, it might have seemed that all forms of matter could be explained as different combinations of fewer than 100 elements, and those elements in turn could be explained as different combinations of protons, neutrons, and electrons. Add photons to the list, and you pretty much had the universe summed up. This is the kind of model physicists like: complicated behavior arising from a few simple building blocks.