Welcome to physics 155. My email is: zacksc@gmail.com
This blog will pay a key role for this class. It will be used for a myriad of communication related to this class. Please check this blog frequently.
Discussion in the comments of this blog is an important part of this class. Peer-to-peer discussion tends to be of great value, particularly in a class like this one where students already share some common physics background. Everyone is expected to contribute. Typically some people use a pen name and some use their real name; either one is fine. Please let me know who you are.
Quantum theory of solids: Solid state physics is essentially the quantum theory of spatially periodic arrangements of atoms. There is no classical theory of solids, just as there is no classical theory of atoms or molecules. The wave nature of electrons, as embodied in the Schrodinger Wave Equation, is critical to understanding systems whose fundamental character depends on non-local, interacting electron wave functions.
Spatial periodicity: Solids are composed of atoms bonded together and, in that sense, they are similar to molecules. However, crystalline solids differ from molecules in that they have a spatially periodic structure (which extends infinitely in our models). This spatial periodicity implies a symmetry, a discreet translational symmetry, which plays a huge role in how one can model and calculate properties of solids. One can model states of a crystal using something called "Bloch states", which involve a linear combination of single-atom states with quantum phase factors that vary in a systematic manner. Bloch-type states provide the starting point for the theory of most properties of solids. Electron states will be a primary focus for us this quarter.
More is different: Solid state physics is one of the most interesting arenas in which to explore quantum theory. It includes branches such as semiconductor theory, which encompasses modern electronics, solar cells, etc., as well as the theories of magnetism, superconductivity and the fractional quantum hall effect. It includes phenomena that can be described using weakly interacting one-electron states, and others where strong electron interaction and collective behavior is critical. At the latter end of that spectrum, the collective phenomena of strongly interacting electron systems, provide a window into the concept of "more is different", which was elucidated by P.W. Anderson in a classic paper in 1972. A hydrogen atom, superconducting aluminum, and living vertebrate animals are all composed of protons, neutrons and electrons. We can comfortably understand the electron in a hydrogen atom and sort of understand the collective phenomena of superconductivity, however, we cannot presume to explain the phenomena of life starting with the Schrodinger equation. We will begin those first steps from the quantum theory of an atom to understanding the quantum theory of collections of atoms know as solids, and a small glimpse into the unexpected phenomena that may arise when many electrons interact and exhibit unanticipated phenomena.
Our first classes will focus on lattice vibrations (phonons) in crystals. Phonons, which are quantized lattice vibrations, are ever present in solids. This topic provides a relatively simple arena in which to begin to explore and understand mathematical modeling of spatially periodic systems. The next post on this blog will begin the discussion of lattice vibrations /phonons. After that I am thinking that we can learn about: electron states in crystals, density of states, specific heat, photo-emission, conductivity, and the nature of metals, semiconductors and insulators. We don't really have a book for this class. Books I have seen recently on solid states physics include: Ibach and Luth, Christman, Aschcroft and Mermin, H.P. Myers.
Background material for this class: Because of the importance of quantum physics to solid state physics it is good if we all have a pretty good grasp of some essential physics of quantum bound states. Length scales, energies and degeneracy are each important. Here are some things that I would like you to review and to be familiar with. Please feel free to comment and ask about these here at this blog (and to add more to this list if you like).
1) An attractive (negative) delta function potential has a single bound state. What is this state? Is its energy positive or negative? What is its functional form? What is its characteristic length scale (size) and where does that come from? What is the relationship between energy and size for this state?
2) Two attractive delta functions (same strength) may have one bound state or two. Why is that? What do they look like? What is their functional form? Does an electron bound to a pair of identical delta function have a higher or lower energy than an electron bound to a single delta function of the same strength?
3) What are the bound states of a finite square well like? Can you sketch them? How many are there? How do their energies compare with those of an infinite square well of the same width. Which states extend farthest outside the well?
4) What is the functional form and quantum size of an electron in the ground state of a 1D harmonic oscillator? What is the relationship between size and the confining potential?
5) For a hydrogen atom, what are the energies, degeneracies and states for the lowest energy levels? What is an s state? What is the difference between a p-type first excited state and an s -type first excited state? what is an example of a p state? an s state? what is a d state? what is an example of a d state?
6) For solid state physics we prefer to work with states that are not Lz eigenstates (though they are usually L^2 eigenstates). Can you construct a spanning set (linear algebra terminology) for the 1st excited states of H that uses only mathematically real states.
7) extra credit: can you construct two real d-states in the 2nd excited states of hydrogen?
Please post your comments, thoughts, questions, etc., in the comment section here.
