PHYSICS 410 FALL 2009

STUDY NOTES FOR EXAM II, Nov. 16, 2009

The exam will be open book, open notes, but no calculators.

Legal notice: although this guide is intended to help you, it is not guaranteed to cover or prepare you for every question on the test.

The exam will cover material (mostly) from Appendix A and Chapter 3, emphasizing the material covered in lecture, in homework, and on the quizzes. I may, however, ask a question from a different point of view; there will be less emphasis on tedious calculation and more on understanding what the material means.

-- Orthogonality of states and superposition of states

-- Expansion of a vector in an arbitary basis; how to find the expansion coefficients

For example, given an arbitrary function f(x) defined on 0 < x < a, do you know how to expand in terms of the eigenstates of the particle-in-a-box?

-- Properties of a Hermitian matrix (operator)

-- similarity and unitary transformations

Do you know how to recognize a unitary transformation? When you are guaranteed a unitary transformation? Do you know the difference between a unitary matrix and a Hermitian matrix?

-- “matrix elements” of an operator in a specified basis

-- general solution for the time-independent Schrodinger eqn given an initial wavefunction.

For example, given H and an initial wfn | Ф >, can you find the solution to

H |Y(t) > = i h (d/dt) | Y (t) > with | Y (t=0) > = | Y (t) >

-- general statistical interpretation; “collapse” of the wavefunction and the probability to find particle in a measured eigenstate.

-- examples in 2 x 2 matrices; finding eigenvalues, eigenvectors of a 2 x 2 matrix.