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.