Modern Physics for Engineers

Problem Set 5

Problem Set - Due in class, Friday, Oct. 30, 1998.

    Problems:
  1. Sketch the following potential:
    	V = Infinity for x<0
    	V = 0        for 0<= x < a
    	V = +V0      for x => a 
    
    After sketching the potential, draw the wave function for the ground state and for the first and second excited states.
  2. SM&M 7-5
    a)	E = hbar^2 Pi^2 / (2 m a^2) (n_x^2 + n_y^2 + n_z^2)
     	
    	For graound state, n_x= n_y = n_z = 1
    
    	E = 3 hbar^2 c^2 Pi^2 / (2 m c^2 a^2)
    	  = 3 (6.582E-16 eV sec 3E8 m/sec)^2 Pi^2 / (2 938.3e6 eV 2E-14^2)
    	  =  1.54E6 eV = 1.54 MeV
    b)	First excited state
    	   n_x = 2 n_y = 1 n_z =1
    	E = 6/3 E_0 = 2 E_0 = 3.08 MeV
    
    	Second excited state
    	   n_x=2 n_y=2 n_z=1
    	E = 9/3 E_0 = 3 E_0 = 4.62 Mev
    
    c) 	Degeneracy:
    	n_x   n_y  n_z
    	 2     1    1
    	 1     2    1    Three fold degeneracy for first excited state
    	 1     1    2
    
    	 2     2    1
    	 2     1    2    Three fold degeneracy for second excited state
    	 1     2    2
    
  3. SM&M 7-11
    a)	|L| ~ l hbar
    -->	l ~ L/hbar = 4.83E31/1.055E-34 = 4.58E65
    b)	fractional change = 1/4.85E65 = 2.2E-66 !!!
    
  4. SM&M 7-12 Mathematica Solution
  5. SM&M 7-23 Mathematica Solution