Lectures: Quantum Mechanics I, 2013

Lecture 1: States, Amplitudes and Interference (August 13, 2013)

The version of the lecture notes with animations is here (do not try to print it). If you want to print a copy for yourself then use this. However, before printing, consider the ecological costs of printing: in terms of trees lost, bleach and other chemicals released into water, the ecological cost of generating energy, the pollution caused in the production of toner, and the eventual disposal of the paper after it is discarded.

Problems 1.1 and 1.2 were solved in the class. Problems 1.3 and 1.4 are left for self-study. They will be discussed in the next class.

Lecture 2: Quanta, Waves and Vector Spaces (August 20, 2013)

The version of the lecture notes with animations is here (do not try to print it). If you want to print a copy for yourself then use this. There are two proofs which are left for you to complete. Also left to you is the Fourier inversion of the Fourier transform of the function which is zero everywhere on the real line except in an interval, where it is unity.

Lecture 3: Vector spaces and Operators (August 22, 2013)

The version of the lecture notes with animations is here (do not try to print it). If you want to print a copy for yourself then use this. The last part of this lecture spills over to the next lecture day. We will discuss density matrices again later.

Problems 3.1, 3.2 and 3.3 (partly) were discussed in the class. The rest of problem 3.3 and problem 3.4 are left for you to tackle.

Lecture 4: The mathematics of 2-state systems (August 24, 2013)

We finished the material from the previous lecture before continuing on to the material for this lecture. The lecture notes are here. The preferred mode of study is to look at the books; consider twice whether you want to print out the notes. The last part of this lecture spills over to the next lecture day.

Lecture 5: The physics of 2-state systems (August 27, 2013)

We solved some problems and finished the material from the previous lecture before continuing on to the material for this lecture. The version of the lecture notes with animations is here (do not try to print it). If you want to print a copy for yourself then use this. The last part of this lecture spills over to the next lecture day.

Lecture 6: The physics of 2-state systems (August 29, 2013)

We completed the left-over material from the previous lecture. This concludes the section on basic quantum phenomena and the 2-state system.

Tutorial 1: Basic linear algebra (August 31, 2013)

The first tutorial concentrated on problems in linear algebra. concludes the section on basic quantum phenomena and the 2-state system.

Lecture 7: Systems with continuous infinity of states (September 3, 2013)

We started on problems where the Hilbert space is infinite dimensional. The particular example was that of a particle moving in a D-dimensional Euclidean space. The printable version of the lecture notes is here.

Lecture 8: Simple one-dimensional potentials (September 5, 2013)

We examined piecewise constant potentials and set up methods to solve arbitrarily complicated such potentials systematically and quickly. New quantum phenomena were encountered. The printable version of the lecture notes is here.

Problems 6.7 and 7.1 must be solved completely before the next lecture, since it will be used repeatedly in the next lecture.

Lecture 9: Simple one-dimensional potentials (September 10, 2013)

We examined band formation in crystals, and the harmonic oscillator. The printable version of the lecture notes is here.

Lecture 10: Simple potentials (September 12, 2013)

We completed the remaining material from the previous lecture; namely, the motion of a charged particle in a magnetic field, and the harmonic oscillator in two dimensions.

Lecture 11: Angular momentum (September 17, 2013)

We completed the remaining material from the previous lecture; namely, the complete symmetry of the harmonic oscillator in two and three dimensions. Then we studied the angular momentum algebra. The printable version of the lecture notes is here.

Lecture 12: Rotations (September 19, 2013)

We completed the remaining material from the previous lecture; namely, the the rotation matrices and tensor operators.

Lecture 13: Adding angular moments (September 21, 2013)

We studied the Hilbert space of two particle systems, and using this we discovered how to add angular momenta, and what Clebsch Gordan coefficients are. The lecture notes is here.

Lecture 14: Units and dimensions (October 1, 2013)

We discussed how to use natural units to understand the basics of quantum phenomena very quickly. The lecture notes is here.

Lecture 20: Spherical symmetry (October 3, 2013)

We discussed how to set up the problem of two particles interacting through a central potential. The lecture notes is here.

Lecture 20: Spherical symmetry (October 8, 2013)

We completed discussion of the problem of two particles interacting through a Coulomb potential. The lecture notes is here.

Lecture 21: Identical particles (October 10, 2013)

We discussed the treatment of multiple identical particles in quantum mechanics. The lecture notes is here.

Lecture 22: Perturbation Theory (October 15, 2013)

We discussed perturbation theory in quantum mechanics, including first order degenerate and non-degenerate perturbation theory. The lecture notes is here.

Lecture 23: Perturbation Theory (October 17, 2013)

We continued discussing perturbation theory in quantum mechanics, with applications to fine and hyperfine structure of spectra. We then set up higher order perturbation theory and discussed an application.

Lecture 24: Entanglement (October 29, 2013)

We discussed entanglement in quantum mechanics, the EPR and Bohm construction, hidden variable theories and Bell's inequality. The lecture notes is here.

Lecture 25: Is perturbation theory exact? (October 31, 2013)

We discussed time-independent perturbation theory for finite dimensional Hilbert spaces, and developed the outline of a proof that perturbation theory is exact. Then we examined the case where the Hilbert space becomes infinite dimensional to undestand how such proofs could fail.

Lecture 26: Path integrals (November 5, 2013)

The path integral formulation of quantum mechanics was introduced. It was applied to the two-state system, the free particle, etc. The lecture notes is here.

Lecture 26: Path integrals (November 9, 2013)

The path integral was evaluated for the harmonic oscillator.