Progressing from the fundamentals of quantum mechanics to more advanced topics, this book provides an examination of many applications that pertain to modern physics and engineering. It begins by discussing the use of Fourier transform pairs to introduce operators in a clear way. In subsequent chapters, the author examines the Schrödinger equation, develops the appropriate operators for angular momentum, gives methods for examining time-dependent systems, and addresses special systems of interest, such as lasers and hadrons. The appendices explore matrices, functions, and physical constants, and give answers to selected problems. Throughout, the author provides relevant mathematical derivations where appropriate.