Problem Set 6, Solution
Physics 143b, Fall 2011
1
Problem 1 - Griffiths 9.11
Rate of an allowed decay transition, |bi |ai is given by Eq. 9.56:
Aba =
03 |p|2
,
30 ~c3
where 0 =
Eb Ea
,
~
and p = qhb|r|ai
Considering the transitions between the following s
Physics 143b, Problem Set 4 Solutions
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2
Note that the following solution (9.1) out of Griffiths solution manual has an incorrect sign (assuming
the standard choice of complex phase in 210 ) in the answer, since H 0 = eEz and not H 0 = eEz, but it
is oth
Physics 143b, Problem Set 1 Solutions
September 20, 2015
1
2
3
To get the exact solution, just note that we have sent 2 = k/m to 2 2 (1 + ). The exact energies
are thus those of the harmonic oscillator, but with a different frequency:
1
En = ~ 1 + n +
2
1
Physics 143b, Problem Set 7 Solutions
Problem 2
Part a
Let us begin with the classical calculation. The Lorentz force F = qv B and so is always perpendicular
to v and B. From these considerations, we conclude that the particle moves at constant speed; v(t
Physics 143b, Problem Set 8 Solutions
1. (a) Squaring the Dirac equation, we obtain
t2 = 2 m2 2 x2 im( + )x ,
and so the Dirac condition is that + = cfw_, = 0, along with 2 = 2 = 1. Since
cfw_i , j = 2ij we may satisfy all the Dirac conditions with = x
Physics 143b, Problem Set 5 Solutions
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2
Problem 3
Part a
In the dipole approximation, we have H 0 = eEx cos(t). Following the derivation in lecture, we need to
consider all states to which the harmonic oscillator can transition with a non-zero matrix el
Final 2010 PHYS 5450
[1] A particle of mass m is free to move in a one dimensional potential V (x) = (x) where > 0.
(a) [5 pts.] What is the physical dimension of ?
(b) [5 pts.] Formulate the boundary condition for the wave-function (x) in x = 0.
(c) [5 p