THESE QUESTIONS ARE RELATED TO QUANTUM PHYSICS. YOU DO NOT HAVE TO HELP WITH ALL QUESTIONS, YOU CAN ONLY PICK WHICHEVER YOU ARE MORE COMFORTABEL TO HELP.

1. Consider an electron (of mass me) moving at 1/4 the speed of light c. (a) Calculate the deBroglie wavelength A of this electron numerically. (b) What is the group velocity v; Elm/(91c of this electron in terms of its A and me? (c) How does the kinetic energy of this electron compare to p3/2mg, where p is its momentum? Note: must take relativistic effects into account. 2. The energy of an electron in a hydrogen atom is: E = p3/2m', - ere-7r; where p is the momentum, r the orbital radius. me the electron mass, 9 the electron charge, and er 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 1/1\"", where d is an integer > 0. (a) Is the boundstate energy always quantized and proportional to 1m2 [where n is an integer > 0)? (b) For the special case of or : 3, are the assumptions for the standard Bohr model still valid