This video provides a short introduction to the specialization quantum mechanics for engineers. Computers have become extremely powerful and affordable, and we increasingly rely on them in both businesses and personal lives. Not only do we use our computers every day, the TVs nowadays have become computers with large screens, appliances are now computer-controlled, car is increasingly use sophisticated software that require significant computing power, and of course, we carry around small computers with us everywhere. Behind this ubiquitous use of computers is the impressive technological development epitomized by the celebrated Moore's law, which captures the exponential growth of computing power sustained over the past few decades. The question, of course, is how to continue this growth? While it is unreasonable to think the semiconductor technology will soon become obsolete, it is equally unreasonable to assume that it will last forever. As the future of computing technology is actively debated, one promising candidate with immense potential has emerged, the quantum computing technology. You probably seen this impressive photo of the quantum computer developed by IBM. By exploiting the quantum nature of microscopic entities such as electrons and photons, quantum computing can potentially perform tasks either impossible or very difficult for classical computers. The revolutionary computing power will accelerate the progress in the forefront of computer science such as machine learning and artificial intelligence. In addition to computing, quantum information technology hold high promises for sensing and imaging that can enable new biotechnology and global positioning systems, for example. Also, a new communication system that is fundamentally unhackable. While the promise of quantum information science and technology is truly exciting, we must also recognize that the current semiconductor technology took decades of development since the first invention of the transistor back in 1947. It is likely that the quantum technology will also take many years, if not decades, to mature. This development will surely require extensive engineering on materials, devices, components, and systems. Unfortunately, most undergraduate engineering curriculum does not include quantum mechanics, making it highly challenging to offer a meaningful graduate-level education on quantum mechanics to engineers. This specialization, quantum mechanics for engineers, is designed to address this need by providing both the foundational materials and quantum mechanics, and the more advanced topics relevant to the emerging quantum technologies. The specialization consists of three courses, foundations of quantum mechanics, theory of angular momentum, and approximation methods. In course 1, foundations of quantum mechanics, we will start by discussing the wave-particle duality and the meaning of wave-functions. We then introduce Schrodinger equation and use it for a variety of one-dimensional potential problems, including potential well, potential barrier and harmonic oscillator. We will then discuss how physical observables are described by operators in quantum mechanics and how quantum mechanics predicts the results of measurements. Here, we will also review the mathematical tools from linear algebra needed for the theoretical framework. Next, we will discuss the time evolution of quantum systems using both Schrodinger picture and Heisenberg picture. Finally, we will introduce the concept of ensembles, then [inaudible] operator to describe pure and mixed ensembles and quantum mechanical particles obeying different statistics, bosons and fermions. In course 2, theory of angular momentum, we will first introduce quantum mechanical definition of orbital angular momentum, by a straightforward extension of classical definition of angular momentum. We will then discuss the electronic states in the hydrogen atom, which are also orbital angular momentum states. We then discussed the rotation operator and how it is fundamentally related to angular momentum. Here, we also introduced the intrinsic angular momentum spin, which has no classical analog. Finally, we developed the general theory of angular momentum, which does not depend on rotational motion, and then discuss the addition of angular momentum, which is important in describing many electronic states, for example, electronic states in atoms. In course 3, approximation methods, we will discuss various approximation methods commonly used in practice. First, we will discuss the time-independent perturbation theory and use it to describe Stark effect and Zeeman effects. We then discussed the time-dependent perturbation theory, which describes the light-matter interaction and leads to the famous Fermi's golden rule. Finally, we discussed other non-perturbative approximation methods which are also commonly used. They include a variational method, tight-binding method, and the use of finite basis set.
