Masayasu AOTANI is an associate professor in the International Center of Kyoto University. He lived in the United States for two decades. With a BS in Chemistry from Kyoto University, 4 years of graduate study in Physics, a Ph.D. in Mathematics from the University of California at Berkeley, and 10 years of experience in industry, he serves as an academic adviser for both the international students and the Japanese students. He is also active in TESOL (Teaching English to Speakers of Other Languages) and currently pursuing a second doctorate in that area. He is the author of an enormously popular book on language learning titled “Eigo Benkyo Ryoku”. He teaches a wide variety of classes at both graduate and undergraduate levels including English language classes, classes to prepare students to study abroad, and physics and mathematics classes where the language of instruction is English.

This course starts with a brief description of Newtonian Mechanics and Maxwell’s Theory of Electricity and Magnetism as contrasted with Quantum Mechanics and Einstein’s Special Theory of Relativity. We will first discuss how old theories break down in the realm of atoms and molecules and at high speeds. The significant roles played by Quantum Mechanics and Relativity in modern physics are explained to put the old and the new physics in a proper perspective. Relativity is briefly explained as a theory to describe physics at speeds comparable to that of light. Quantum Mechanics is introduced as a device to solve the problems classical theories faced in explaining microscopic phenomena. Having given a grand framework of the current state of affairs in physics, we then specialize to Quantum Mechanics. Planck’s idea of quantum, Einstein’s explanation of photoelectric effect, Bohr model, and de Broglie’s matter wave all set the stage for an introduction of the Schrödinger Equation. The meandering path to the equation is presented in full to give the students a taste of how actual dirty work is done in physics. We then apply the theory to simple systems involving the infinite square well potential, a barrier potential, and the simple harmonic oscillator. In the process, analytical skills to solve second order partial differential equations like the Schrödinger Equation are developed. The course ends with a full solution for the hydrogen atom, and the predicted results are compared with the outcomes of actual experiments. This provides a justification for the nebulous and potentially even dubious process of the development of quantum mechanics. By highlighting the difference between purely theoretical science like mathematics and a basically experimental science like physics, students can acquire an understanding of the role of physics in a larger context of the human pursuit of knowledge and truth.

#1 Classical Physics and Modern Physics
#2 Schrödinger’s Theory of Quantum Mechanics
#3 Max Born’s Interpretation of Wavefunctions
#4 Time-Independent Schrödinger Equation
#5 Solutions of Time-Independent Schrödinger Equation
#6 Solutions of Time-Independent Schrödinger Equation
#7 Solutions of Time-Independent Schrödinger Equation
#8 The Hydrogen Atom
#9 The Hydrogen Atom
#10 The Hydrogen Atom
#11 The Hydrogen Atom
#12 Final Examination

[Resources]

Robert Eisberg, Robert Resnick : Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles 2nd edition, Wiley, 1985