THESE QUESTIONS ARE RELATED TO QUANTUM PHYSICS: PHY256

1. Consider an electron (of mass me) moving at 1/4 the speed of light 0. (a) Calculate the deBroglie wavelength A of this electron numerically. (b) What is the group velocity v; Btu/8k of this electron in terms of its A and me? (C) How does the kinetic energy of this electron compare to p2/2me, where p is its momentum? Note: must take relativistic effects into account. 2. The energy of an electron in a hydrogen atom is: E = p-'/2m,_, - ae-Vr; where p is the momentum, r the orbital radius, me the electron mass, 9 the electron charge, and a the Coulomb constant. Use the uncertainty principle for momentum vs. position to estimate: (a) the minimum radius; (b) the momentum corresponding to this radius. 3. Consider the l51 excited state of a particle of mass m in a 1D innite-potential well of width L. (a) Calculate the expectation values for position, momentum and kinetic energy. (b) Is the momentum and is the total energy well dened? 4. Consider a generalized Bohr model, whose force is proportional to l/r\