Physics 591 - Homework Set # 1 Due: Monday, August 30 5 pm 1. Consider the set of real valued, two by two matrices. a) Show that this set is a linear vector space with the vector addition operator being matrix addition and give the dimension of the space.
Physics 591 - Homework Set # 2 Due: Wednesday, September 8 5 pm 1. Consider the matrix
a) Show that it is unitary b) Find its eigenvalues c) Find the corresponding eigenvectors and show that they are orthogonal d) Verify that is a diagonal matrix with U b
Physics 591 - Homework Set # 3 Due: Monday, September 13 5 pm THIS HOMEWORK MUST BE DONE BY HAND, NO MATHEMATICA ALLOWED! 1. Consider a system in which there are only two linearly independent states. In some basis these states are
the system is in a state
Physics 591 - Homework Set # 4 Due: Monday, September 20 5 pm 1. Consider example 4.2.1 discussed in class. In the basis in which is given by is diagonal the operator
there are 1000 particles in a state
a) Find the expectation value for b) Now assume that
Physics 591 - Homework Set # 5 Due: Monday, September 28 5 pm 1. In class we considered the problem of a particle of mass m that is conned to exist on a circular ring of circumference a. We solved the eigenvalue problem for this, and our solution in class
Physics 591 - Homework Set # 6 Due: Monday, October 4, 5 pm 1. In class we proved a theorem stating that one-dimensional bound state problems are not degenerate. However, in another class we discussed the case of the particle that slides without friction
Physics 591 - Homework Set # 7 Due: Monday, October 11, 5 pm
1. (7.3.5) a) Using symmetry arguments show that (for the harmonic oscillator) and thus that in these states. Show that
Show that the ground state saturates the uncertainty bound b). (7.3.6) Con
Physics 591 - Homework Set # 9 Due: Monday, October 25, 5 pm 1. Consider a particle subject to a constant force f in one dimension. Solve for the propagator in momentum space to get
Transform back to coordinate space to get
2. Verify that
agrees with the