hw4 - PHY 4604 Fall 2010 Homework 4 Due by 5:00 p.m on...

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PHY 4604 Fall 2010 – Homework 4 Due by 5:00 p.m. on Monday, October 18. Please deliver your homework to NPB 2162, or push it under the door if the room is unoccupied. No credit will be available for homework submitted after the start of class on Friday, October 22. Answer all three questions. Please write neatly and include your name on the front page of your answers. You must also clearly identify all your collaborators on this assignment. To gain maximum credit you should explain your reasoning and show all working. 1. A particle of mass m moves in the one-dimensional potential V ( x ) = - V 0 ( x ) , where V 0 > 0 is an energy and a > 0 is a length scale. The bound state wave function for this problem was discussed in class; see also Eq. (2.129) of Griffiths (where α V 0 a ). (a) Find h V i , the expectation value of the potential in the bound state. (b) Find h T i , the expectation value of the kinetic energy in the bound state, where ˆ T = - ( ~ 2 / 2 m ) 2 /∂x 2 . Verify that h T i + h V i = E , the energy of the bound state.
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