For a spin 1/2 system in a state that is expressed in terms of the base kets of the sz operator. construct the unitary operator u for the basis transformation from the sz basis to the (sz + sy)/sqrt(2) basis. write your answer as an operator and the matrix representing the operator in the sz basis. check your result by transforming the |sx; +> ket from the sz basis to this new basis. what should you expect the result will look like?

Intro: a solid ball of radius rb has a uniform charge density ρ. part a: what is the magnitude of the electric field e(r) at a distance r> rb from the center of the ball? express your answer in terms of ρ, rb, r, and ϵ0. part b: what is the magnitude of the electric field e(r) at a distance r express your answer in terms of ρ, rb, r, and ϵ0. part c: let e(r) represent the electric field due to the charged ball throughout all of space. which of the following statements about the electric field are true? check all that apply. e(0) = 0 e(rb)=0 limr→∞e(r)=0 the maximum electric field occurs when r=0 the maximum electric field occurs when r=rb the maximum electric field occurs as r→∞.