Problem 3.24 Show that if an operator Ö is hermitian, then its matrix elements in any orthonormal basis satisfy Qmn Qnm: That is, the corresponding matrix is equal to its transpose conjugate.

4. Compare and contrast electric domain walls to magnetic Bloch walls. Consider such items as wall thickness, direction of polarization or magnetization, and factors that influence on each.

A charged nonconducting rod, with a length of 2.52 m and a cross-sectional area of 4.76 cm², lies along the positive side of an x axis with one end at the origin. The volume charge density p is charge per unit volume in coulombs per cubic meter. How many excess electrons are on the rod if p is (a) uniform, with a value of -4.66 µC/m³, and (b) nonuniform, with a value given by p= bx², where b = -2.18 µC/m²? (a) Number i (b) Number i Units Units

The assembly shown below consists of a brass shell (1) fully bonded to a ceramic core (2). The brass shell [E = 115 GPa; α = 18.7 x 10-6 /°C] has an outside diameter of 50 mm and an inside diameter of 35 mm. The ceramic core [E = 290 GPa; α = 3.1 x 10-6 /°C] has a diameter of 35 mm. At a temperature of 15°C, the assembly is unstressed. Determine the largest temperature increase that is acceptable for the assembly if the normal stress in the longitudinal direction of the brass shell must not exceed 80 MPa.

Use a sketch, an equation in addition to your precise and concise description. Discuss the quantum description of the beam splitter