Physics 472
Problem Set 1
Spring 2013
1. For a fixed , the nth radial wave function for a particle confined in a spherical infinite well of radius a is 2 1 Rn (r) = j (n r/a) , 3 |j a +1 (n )| where n is the nth zero of j (). (a) (5 pt) Using n0 = n, plot
Homework Set #5 /1/ Exercise 9.17. /2/ Exercise 10.1. /3/ Exercise 10.2. /4/ Exercise 10.3. /5/ Exercise 10.6. /6/ Exercise 10.8. /7/ Exercise 10.9.
due Wednesday February 15
/8/ FLIP COIL. As the coil of copper wire is flipped over, a total charge Q goes
Homework Set #4 /1/ Exercise 9.12. /2/ Exercise 9.13. /3/ Exercise 9.15. /4/ Exercise 9.18. /5/ Exercise 9.22. /6/
due Wed Feb 8
/7/ Dielectric screening. Two charged particles (charges +q1 and +q2) separated by distance r in vacuum experience forces dire
Homework Set #3 /1/ Exercise 9.1. /2/ Exercise 9.3. /3/ Exercise 9.4. /4/ Exercise 9.5. /5/ Exercise 9.6.
due Wed Feb 1
/6/ The cylindrical bar magnet. Consider a uniformly magnetized cylinder, with radius a and height h. The magnetization is M(x) = M k f
Homework Set #2 /1/ Exercise 6.5. /2/ Exercise 6.6. /3/ Exercise 6.8. /4/ Exercise 6.11. /5/ Exercise 6.19. /6/ Exercise 6.21.
due Wed Jan 25
/7/ Two parallel conducting plates (both parallel to the xy-plane) are charged with equal but opposite charges +Q
Physics 472
Problem Set 12
Spring 2013
49. The partial wave expansion for the scattering amplitude f () is f () = 1 k
=0
(2 + 1)ei sin P (cos ) .
With the expression for the total cross section T = d|f ()|2 ,
use the partial wave expansion to show that T
Physics 472
Problem Set 11
Spring 2013
45. A two level system with energy levels E1 , E2 , E2 > E1 is perturbed by a time-dependent interaction H (t) with H11 = H22 = 0 and H12 (t) = H21 (t) = V e-t , where V, are constants and t 0. (a) Compute the amplit
Physics 472 41. Griffiths 9.1 42. Griffiths 9.5.
Problem Set 10
Spring 2013
43. Expand the exact solution for C1 (t) corresponding to H12 (t) = V (t) to second order in (2) |V |2 /( 2 0 ) and compare the result with the expression for C1 (t) obtain in cla
Physics 472
Problem Set 9
Spring 2013
37. The general result for the weak field Zeeman effect can be obtained by using the angular wave functions
j
mj (, )
=
+ mj + 1 mj - 1 2 2 Y + + 2 +1 - mj + 1 mj - 1 2 2 Y + - 2 +1
- mj + 1 mj + 1 2 2 Y - for j = +
Physics 472
Problem Set 8
Spring 2013
33. Griffiths 6.37 (n=3 Stark effect) Presumably, you have identified the non-vanishing matrix elements given in (a). You can use the given values to answer (b). Mathematica is probably the way to go for this problem.
Physics 472
Problem Set 7
Spring 2013
28. (a) Given that a measurement of y component of the electron's spin will yield either 1 h 2 1 or - 2 h, compute the normalized eigenvectors of Sy . (b) At time t = 0 an electron is in the state (0) = cos() sin() .
Physics 472
Problem Set 6
1 2
Spring 2013 is
23. The wave function for a 3p electron in the 2 P 1 multiplet with mj =
2
2 1 = R31 (r) Y (, )- - 3 1 Suppose the coefficient of
1 0 Y 3 1 +
1 0 Y + . 3 1
is changed from -1 to i. What are the possible results
Physics 472
Problem Set 5
Spring 2013
19. A system of two spin 2 particles is in the state | given by | = |j1 m1 |j2 m2 = |2 2 |2 -2 , (a) (3 pt) If the z-component of the total angular momentum, Jz , is measured, what values would be obtained and what is
Physics 472
Problem Set 4
Spring 2013
15. (10 pt) When orbital angular momentum is added to angular momentum 1 the resulting 2 1 total angular momenta are j = + 1 , - 1 . In the case of j = - 2 , the state with the 2 2 largest value of mj is ( - 1 , - 1 )
Physics 472
Problem Set 3
Spring 2013
10. (a) 1pt, (b) 3 pt, (c) 3 pt, (d) 3 pt) Griffiths 4.27. 11. (10 pt) Griffiths Problem 4.31. 12. An electron in the initial state (0) = cos(/2) sin(/2)
moves in a uniform magnetic field B oriented in the z direction
Physics 472
Problem Set 2
Spring 2013
5. We showed that Y (, ) = A sin ei . (a) (4 pt) For = 1, determine A1 by normalizing Y11 (, ). ( + 1) - m(m - 1)| m-1 , derive Y10 (, ) and Y1-1 (, ). (b) (6 pt) Using L- | m = h
6. (10 pt) The Hamiltonian for a lin