Homeworks are in the notes. You should read the notes carefully to make sure you do not miss the homeworks. These are due every week, on Wednessdays.

Part I: Fundamental concepts
1. Course Outline
2. Handout: Linear algebra
   


Experimental considerations that provide a rationalization for the postulates of quantum mechanics.
3. The Stern-Gerlach Experiments To test the Stern-Gerlach experiments, download this nifty java applet. It will allow you to run the Stern-Gerlach experiments on your computer and understand it better. (You will need to have Java installed and enabled for this to run from the browser.) Click on the help menu to customize experiments.
4. The Stern-Gerlach experiments explained using plane polarized light and circularly polarized light
5. A brief summary of Stern-Gerlach experiments
6. de Broglie's Wave particle duality


Formal considerations that rationalize the Stern-Gerlach experiments and eventually lead us to the postulates of quantum mechanics.
7. Representation theory, Dirac notations, Hilbert space
8. Introduction to operators, Discrete and continuous representations, Coordinate and momentum representation, the quantum-mechanical Wavefunction
   The following additional material is related to what we have learned thus far. Hence please go over these yourself. We will cover it later in class, quickly. If you have trouble see me. You are responsible for the homework problems in these sections.
   Simultaneous additional reading: Important Summary of Dirac notation
   Simultaneous additional reading: Theory of Operators: I
   Simultaneous additional reading: Pauli Spin matrices
   Simultaneous additional reading: Change of basis
   Simultaneous additional reading: The Concept of Measurement in quantum mechanics
9. Postulates of Quantum mechanics
   Homework: Justify the stated postulates through your knowledge of the Stern-Gerlach experiments.


The statement on "uncertainty" is really a result of the vector spaces idea that we have discussed above.
10. Simultaneous observables, Commutation relations, expectation values
11. Uncertainty Principle and Coherent states


The Schrodinger Equation and associated properties.
12. The Time dependent Schrodinger Equation
    Simultaneous additional reading: Solving the time-dependent Schrodinger Equation.
    Simultaneous additional reading: The Classical limit and the WKB theory
    Simultaneous additional reading: Probability Current and the continuity equation.
    Simultaneous additional reading: Dirac quantization, The Schrodinger picture and the Heisenberg Picture, Heisenberg's equation of motion (The Heisenberg's equation of motion is analogous to the time-dependent Schrodinger Equation, but as we see here provides connections to classical mechanics as well)
    At this point you may wish to read a little about the history of quantum mechanics . The link above oulines some of the struggles between Schrodinger and Heisenberg in arriving at a unifying picture of quantum mechanics. It is Dirac's path that we have chosen in this class, which does unify the two pictures. In addition, through the set of readings provided here, you may see that the connections to classical mechanics can be quite exciting.
13. The Time independent Schrodinger Equation.
    Simultaneous additional reading: Theory of Operators: II. Hermitian operators and their properties.


Part II: Analytically solvable model problems for free-particle
14. Particle-in-a-box