Please be very clear in your solutions thank you for the help!

Please be very clear in your solutions thank you for the help!
Introduction to Quantum Physics (PHY256) Homework: # 4 Due: April 6th Problem 1: Free particles and relativity. (a) Using the relativistically correct relationship between mass energy and momentum determine the relationship between ? and k. (hint: continue to assume a plane wave for the wavefunction) (b) Using your result in (a) show that the group velocity is: (c) For this part assume the relationship p=hk still holds and use the relativistic relationship between velocity and momentum. What is the relationship between the group velocity and the particle velocity? (d) Using the relativistically correct expression for energy and momentum determine the phase velocity of a massive particle. (e) Is the phase velocity less than or greater than the speed of light? Problem 2: Scattering off a potential well: A particle of mass m and energy E moves in a region where there is initially no potential energy encounters a dip in the potential of length L and depth U0. See picture below: a) Show that the reflection probability is: b) Plot R for 0

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