Physics 139a Syllabus.

Grading will be based on HW (20%), midterm1 (25%), midterm2 (25%) and final exam (30%).
1st midterm date:April 23
2nd midterm date: May 28
final exam: Wednesday, June 12, 12-3:00 PM
Book: Griffiths, Intro to QM, 3rd edition. We will start with chapter 2.

Class is from 1:30 to 3:05 PM on Tuesday-Thursday. My regular office hours will be 11:30 to 12:30 PM on Wednesday and after class on some days as needed. My email is zacksc@gmail.com

Expect weekly homework.

Sections: TA Michael Saccone will have sections and office hours as follows:
Tuesday: 10:25 to 11:25 AM, office hours in ISB 292
Tuesday: 3:30 to 5:20 PM, section in Thimann 391
Wednesday: 1:20 to 2:25 PM, office hours in ISB 292
Wednesday: 2:40 to 5:05 PM, section in ISB 235

Welcome to 139a

In this class we will study the behavior of electrons. We do that using the Schrodinger wave equation. (I believe that equation was originally known as “the wave equation”. Later, it became known as the “Schrodinger equation”. Some notable things are:  it is a wave equation, it has an hbar multiplying the spatial derivative, and, the time derivative is a 1st derivative, not a 2nd derivative, which is important.)

In physics we often study the time evolution of things. The time dependence of an electron wave function can be obtained by writing the wave-function as a sum of eigenstates (energy eigenstates), which each have a time-dependent phase factor. (Phase is important in wave theories.) We will spend a lot of time in this class finding eigenstates, talking about eigenstates, and calculating things using eigenstates. We will learn about the eigenstates of infinite square wells, harmonic oscillators, finite square wells, delta function potentials and hydrogen atoms. We will use these eigenstates to model time-dependence and to calculate expectation values. We will also look at the eigenstates of a free electron and use them to make a wave packet which is spatially localized and moves at a characteristic velocity.

One of the really interesting aspects of quantum physics is the kinetic energy. When we study the traveling wave packet, we will see that there are two kinds of kinetic energy. One is associated with motion (like classical K.E.).  The other is a quantum kinetic energy, associated with confinement, which, like quantum spin, has no classical analogue.  This quantum kinetic energy plays a huge role in the phenomenology of electrons, atoms, molecules and lots of important things.

We will learn what determines the size of a hydrogen atom, why an electron in a finite square-well has a lower ground-state energy than an electron in a comparable infinite square well, as well as how the bound states of a one-dimensional harmonic oscillator and an infinite square-well are essentially similar. We will study the role of symmetry and degeneracy in influencing the nature of hydrogen atom eigenstates, chemical bonding, and the periodic table. We will introduce the puzzling and elusive concept of quantum spin, a property with no classical analogue. We will follow the inexorable path from de Broglie’s suggestion to Schrodinger’s wave equation and explore some of the interesting phenomenology that flows from that.

Here is a week-by-week outline, subject to revision:
Notes:  weeks 1-5. QM in one dimension (1D); weeks 1-8 focus on the theory of a single electron in different circumstances (i.e., potentials)

week 1. infinite square well, expectation values, kinetic energy and confinement
week 2. harmonic oscillator, emergence of a quantum length scale.
We will use a Hermite polynomial approach and not raising and lowering operators. We will do expectation value calculations for position, size, kinetic and potential energy and involving time dependence.  (Later in the quarter we will return to the harmonic oscillator potential and learn about raising and lowering operators.)
Also, the time-independent Schrodinger equation. We will derive that from the Schrodinger Wave equation using separation of variables.
week 3. finite square well, delta function. Relaxing the boundary allows the wave-function to spread out somewhat and reduces K.E.
A finite square well has some bound states, but not an infinite number. We will explore how to use the time-independent Schrodinger equation and boundary conditions to obtain low-energy eigenstates for the square well. We will look at the degree to which states extend outside the well in terms of probability density. We will examine the reduction of kinetic energy associated with de-localization and the price that is paid for that in P.E.
week 4. formalism, linear algebra, orthogonality, linear independence, how eigenstates form an orthonormal basis of a Hilbert space.
Please review the concepts and applications of orthogonality, linear independence and inner products. Understand what a basis is. Review Hermitian matrices and how their eigenstates can be used as a basis (orthogonal) (and that their eigenvalues are real). Review trace and how the trace of a hermitian matrix is invariant…
week 5. free electron, traveling wave packet, kinetic energy, scattering, tunneling
week 6. 2D harmonic oscillator, constructing and normalizing 2D states, angular momentum, symmetry, hydrogen atom state, the size of the hydrogen atom
week 7. hydrogen atom 2, excited states, sp2 wave-functions, interaction of electromagnetic radiation (light) and electrons, stimulated transitions between states
week 8. hydrogen atom 3, size, bonding, symmetry and the periodic table
week 9.  spin, states involving more than 1 electron
week 10. review