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)