note01 - Introduction to Quantum and Statistical Mechanics...

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1 Introduction to Quantum and Statistical Mechanics Fall 2009 Handout 1 Classical Mechanics and Wave Mechanics as Asymptotic Cases for Quantum Mechanics: The Wave-Particle Duality for All Matters Complementary Reading: Introduction (pp. ix – xi), Chaps. 1-3 (pp. 1-42), Hagelstein, Senturia and Orlando. 1.1 Learning Quantum Mechanics: Reasons and Methods Quantum mechanics is the cornerstone of the physics behind atoms, electrons, photons and phonons (quantization of thermal energy), and deviates from classical mechanics significantly when the mass is small or negligible. In the modern world, it is important for engineers to manipulate electrons and photons, as they are the most efficient way to transfer energy and information. The interaction of atoms and electrons brings the chemistry world, where absorption and loss of electrons are called reduction and oxidation (redox). The interaction of atoms and photons brings the photochemical cells, which sustains the biological world that we know through photosynthesis. The interaction of electrons and photons brings the field of optoelectronics, where lasers, solar cells, imaging, etc., are an essential part of our daily life. You can learn many industrial design principles in a company, but a professional career will seldom have the opportunity to teach you quantum mechanics. More importantly, this class will teach you how to think about the reality of this world in a more universal way, which joins not only particles and waves, but also deterministic and probabilistic points of view. Quantum and statistical mechanics are (un)fortunately hidden behind complex mathematics of calculus, complex variables and probability. For what we know now, the most basic formulism still needs an in-depth treatment of partial differential equations, Fourier transforms and probability. From that viewpoint, as Feynman put it, you need to learn quantum mechanics with a pen . Before you comprehend the physical meaning, you need to follow through the math once for the derived expressions to sink in, fully convinced in your mind. You should then make observation about what has been achieved, “internalizing” the physical meaning. Another important attitude to learn quantum and statistical mechanics is to keep your curiosity high, even amidst considerable amount of mathematical derivation that seems tedious. In that process, keep asking yourself: “What will come out of the basic formulation?” “How does the formulation reflect the experimental reality that deviates from the classical mechanics?” After you have mastered the concept of quantum and statistical mechanics, not only you have a good foundation for the modern electronics, optoelectronics, and nanotechnology, but also you should feel proud of yourself that you have now joined the brightest minds of our generation.
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This note was uploaded on 11/26/2010 for the course ECE 3060 at Cornell University (Engineering School).

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note01 - Introduction to Quantum and Statistical Mechanics...

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