V.2. A crystalline insulator is placed in an electric field E. An electron in the crystal will oscillate according to e(x -x. ) E = 8(k, + eEt/h)-8(k,) where & and k are the energy and momentum of the electron. (a) Estimate a typical amplitude for the oscillation, and a typical period. (b) For an electron moving in a periodic potential of a superlattice with the miniband width & = 10 meV and lattice spacing A = 50 A in an electric field E = 103 V/cm, calculate, neglecting the electron scattering, the amplitude in real space and the frequency of the Bloch oscillations. (c) What should be the electron relaxation time r to observe these oscillations