Aparticle moving in one dimension is described, at some instant in time, by the wavefunction where f(z) is a real-valued function of and k is a constant a) what is the physical interpretation of the quaatity where a and b are constants? mar b) explain the meaning of the term "expectation value". what is the physical inter- pretation of each of the following quantities: and marks c) show that the quantity b is independent of the function x) if f(oo) 0 and determine its value in terms of nark d) sketch the real part of ψ(z) if /(z) = exp(-x2/r2) where r is a constant and 1 . indicate those features of your sketch that depend on k and r. kr mar e) without calculation, briefly explain what happens to this wavefunction as time advances, 3 marka)

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