Consider a particle in a state desernbl dy ψ=ne-ar(r + y + 22), where α > 0 and n is a normalization factor (a) show, by rewiting the yi, m functions with m-0,±1 in terms of x, y, z, and r, that , and y,0 4t (b) using the result of (a); evaluate the probabilities for obtaining t - h, 0, and -h, respectively, in a measurement of, for a particle described by ψ above.

To understand the electric potential and electric field of a point charge in three dimensions consider a positive point charge q, located at the origin of three-dimensional space. throughout this problem, use k in place of 14? ? 0. part adue to symmetry, the electric field of a point charge at the origin must point from the origin.answer in one word.part bfind e(r), the magnitude of the electric field at distance r from the point charge q.express your answer in terms of r, k, and q. part cfind v(r), the electric potential at distance rfrom the point charge q.express your answer in terms of r, k, and q part dwhich of the following is the correct relationship between the magnitude of a radial electric field and its associated electric potential ? more than one answer may be correct for the particular case of a point charge at the origin, but you should choose the correct general relationship. a)e(r)=dv(r)drb)e(r)=v(r)rc)e(r)=? dv(r)drd)e(r)=? v(r)r