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Assignment 9

# Assignment 9 - University of Florida Department of Physics...

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University of Florida Department of Physics PHY3101, Fall 2009 Introduction to Modern Physics Homework 9 - Due Fri, Mar 05 2009 Student Name: ( please print large and legibly. No UFID is necessary. ) Total: / 30 points.

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Physics 3101, HW#9, Fri, Mar 05 2009 Name: Problem 1: Quantum Mechanical Tunneling (4 points) The coefficient of transmission across a potential barrier (shown in the figure) is given by T = | F | 2 | A | 2 = 1 + sinh 2 ( αa ) 4 E V 0 1 - E V 0 - 1 x x = 0 x = a V(x) V 0 E < V 0 II : V=V 0 III : V=0 I : V=0 Figure 1: (a) Show that if αa 1, then the equation simplifies to T 16 E V 0 1 - E V 0 e - 2 αa ( 4 points ) 1
Physics 3101, HW#9, Fri, Mar 05 2009 Name: Problem 2: Angular Momentum (5 points) Show that angular momentum ~ L is conserved for a particle moving in any spherically symmetric potential (i.e. V is only a function of r). Hint: Show that d ~ L/dt = 0 . 2

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Physics 3101, HW#9, Fri, Mar 05 2009 Name: Problem 3: Angular Momentum (10 points) The angular momentum operator is defined as L op = - i ~ ( ~ r × ~ ), where ~ = ∂x , ∂y , ∂z in cartesian coordinates. The z-component of the angular momentum operator is L z op = - i ~ ( ~ r × ~ ) z . Show that in spherical coordi-

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Assignment 9 - University of Florida Department of Physics...

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