Outline and expectations ...

Welcome to physics 139a. This class weaves together 3 themes which could be loosely characterized as:

1) quantum formalism, postulates, mathematical underpinnings and structure,

2) quantum physics in 1-dimension (mostly bound states),

3) quantum physics in more than 1-d (2 & 3), focusing particularly on the hydrogen atom with its interesting and unusual degeneracies, etc.

One could imagine covering 1) before 2) or 3); but that would probably be overly formal, slow, and pedagogically disastrous. Instead we will try to weave the formalism into 2) and 3) so that we will have concrete examples to work with along the way, and so that we will be able to get as far as we need to in this 1 quarter, 10 week class. The material on the hydrogen atom at the end of the quarter is important both for people planning to take 139b and for those taking this as their last class in quantum.

Quantum physics is amazing and provides the underpinning for most of physics, chemistry and more. It is primarily the story of the electron. We endeavor to develop an integrated mathematical and intuitive understanding of this magnificent small creature which, when confined, acquires significant kinetic energy. This simple and unusual trait plays a central role in many quantum phenomena of importance.
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Background:

Linear algebra is exceedingly important to QM (see problems in HW post below). The more you know about finite-dimensional linear algebra (basis sets, inner products, spanning, linear independence,...) the better. As the book (Liboff) discusses in 4.4, QM is based on Hilbert spaces, which are a infinite dimensional analogue to finite-dimensional vector spaces. Most of the same concepts carry over. Speaking of finite dimensional vector spaces, we will use those too, and an intimate familiarity with hermitian matrices and their eigenvalues and eigenvectors is essential.

Where we will start:

We will start with the wave equation (now called the Schrodinger eqn.) for electrons. With that and other starting postulates we will do separation of variable, talk about time dependence, normalization, expectation values, ... and get into some examples with the infinite square well and other 1-d potentials including: the attractive delta-function, the finite sq well and the harmonic oscillator. In addition to learning how to calculate things, it is valuable for you to develop a sense of aesthetics. What is appealing or useful with each of these potentials?; what are their flaws, weaknesses or ...?

For more, see the April 1 post, Outline and road map.