Continuing size reduction in mesoscopic and nanoscopic electronic, photonic, and plasmonic devices makes the employment of quantum physics (QP) and quantum electrodynamics (QED) inevitable. Engineers at the forefront of these fields increasingly need to have a working knowledge of QP and, more importantly, feel confident to manoeuver through the intricate calculations involved. However, electrical engineers and applied physicists are typically unfamiliar with the sophisticated mathematical apparatus in QP and QED, which is generally perceived to be formidably abstract.The Mathematical Quantum Physics for Engineers and Technologists volumes aim to explain the mathematical foundation of QP and QED to engineers using an engineer's mindset as the starting point, and following a new line of thinking based on clarity and obviousness. Written for an audience of researchers and advanced students in electrical engineering, computer science, applied mathematics and applied physics, the Mathematical Quantum Physics for Engineers and Technologists volumes guide readers towards acquiring a solid understanding of the mathematical intricacies of quantum physics and quantum electrodynamics.Volume 1 covers topics including the resolution of identity, generalized functions, bases, dual bases, frames, dual frames, generalized transforms and inverse transforms, operator gymnastics, canonical commutation relationships, standard and generalized creation and annihilation operators.