Problem 4: (a) There is a full symmetry between the position operator and the momentum operator. They form a conjugate pair. In real-space momentum is a differential operator. Show that in k-space position is a differential operator, ih, by evaluating expectation value (x)=fdxy (x)xy(x) in terms of (kx) which is the Fourier transform of (x). брх (b) The wave function for a particle in real-space is u(x,t). Usually it is assumed that position x and time t are continuous and smoothly varying. Given that particle energy is quantized such that E = hw, Show that the energy operator for the wave function (x,t) is, ih.