Quantum Mechanics I


Studying physics can be likened to Carpentry where using the right type of tool makes the job less tedious. The invention of quantum mechanics during the first 27 years of the twentieth century marked a revolutionary change in our understanding of phenomena on microscopic scales. Classical physics ideas held before then had instant limitations in their validity, as quantum mechanics became an alternative theory more richer both in scope and application. Although crucial to the understanding of quantum mechanics, we will not discuss the inadequacies of classical physics but will immerse ourselves directly into “a quantum-mechanical approach to thinking”.

At a glance, quantum mechanics (QM) is a mathematical tool for predicting the behavior of the microscopic world and hence help us in understanding how this affects the macroscopic world around us. However, QM cannot be understood without developing appropriate requisite mathematical tools. Doing so would be similar to telling you to drill a well using a chisel. But QM is generally a difficult theory and solutions to standard textbook problems are relatively few and mostly approximations. I therefore suggest as a rule of thumb that its prudent to give you a shovel and instruct you to start digging yourselves. It may make your hands develop blisters at first, but its the only excellent and efficient way to learn QM. Indeed “one cannot discuss what QM means without developing a firm sense of what it does”.This course will provide you with an overview of the basic theory needed to do modern QM as well as introduce you to basic applications of QM and the commonly used approximation methods. It is assumed that you are familiar with rudimentary basics on: Linear Algebra, Complex numbers, Partial Differential equations, Fourier Analysis, Dirac Delta notation, elementary Classical Mechanics as well as some Electrodynamics concepts.

NOTE: The more knowledge of Mathematics and Physics you have, the much easier it will be to do QM and the more you will gain from the course. Reviewing of basic concepts in QM from the recommended texts is highly encouraged. 

The aim of this course is to enable the learner develop special techniques for attacking more advanced realistic problems in QM that apply to microscopic phenomena and associated research. Familiarity with basic concepts covered in an undergraduate level QM course- from historical developments such as the Planck's radiation law, Einstein's Debye theory, the Bohr atom, de Broglie matter waves, the Compton effect, Frank-Hertz experiment, Davisson-Germer-Thompson experiment- to modern concepts such as the wave functions and its physical interpretation, the uncertainty principle, Hilbert Space, Dirac Notation etc will be assumed. For the learners who would wish to thesis research in theoretical Physics, a more advanced course in QM that will consider more challenging topics, will be offered in the second semester, and this course will form a useful pre-requisite. For a good review of undergraduate QM read chapters 1-3 in the text: Introduction to Quantum Mechanics by D. J. Griffiths (2004).

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