ProblemSet1 - Ch21a
Fall
2009
 Problem
Set
1


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Unformatted text preview: Ch21a
Fall
2009
 Problem
Set
1
 TA:
Sigrid
Barklund
 Due:
October
14,
2009
at
1pm
 
 Collaboration
with
other
students,
notes
from
this
year,
and
quantum
mechanics
textbooks
 are
encouraged,
but
the
answers
you
turn
in
must
be
your
own
work.
Use
of
solutions
 manuals,
problem
sets
from
previous
years,
and
internet
resources
are
not
allowed.
Please
 note
how
much
time
you
spend
working
this
problem
set
when
you
turn
it
in.
 
 1. Blackbody
Radiation.

 Find
the
wavelength
corresponding
to
the
maximum
in
the
Planck
distribution
for
a
 given
temperature,
and
show
that
the
expression
reduces
to
the
Wien
displacement
 law
at
short
wavelengths.
Determine
an
expression
for
the
constant
in
the
law
in
 terms
of
fundamental
constants.
(This
constant
is
called
the
second
radiation
 constant.)
 
 2. Photoelectric
Effect.
 The
work
function
of
platinum
is
5.65
eV
(To
what
physical
property
does
this
 correspond?)
What
is
the
minimum
frequency
of
light
required
to
observe
the
 photoelectric
effect
on
Pt?
If
light
with
a
150
nm
wavelength
is
absorbed
by
the
 surface,
calculate
the
kinetic
energy
and
de
Broglie
wavelength
of
the
emitted
 electrons.
 
 3. Particle­Wave
Duality.
 In
an
electron
diffraction
experiment,
a
monoenergetic
beam
of
electrons
is
 elastically
scattered
from
a
Ni
crystal
face
into
a
detector
at
an
angle
θ.
The
electron
 beam
is
normal
to
the
surface,
and
θ
is
the
angle
between
the
incident
electron
beam
 and
the
scattered
electrons.
 
 a) If
the
crystal
lattice
is
a
regular
simple
cubic
array
of
atoms
with
a
nearest
 neighbor
spacing
of
d,
and
the
electrons
are
of
sufficiently
low
energy
that
 penetration
of
the
electrons
in
the
crystal
is
negligible,
derive
an
expression
 describing
the
observed
diffraction
pattern.
 b) It
was
found
experimentally
that
for
electrons
of
energy
54.0
eV,
the
most
 intense
diffraction
peak
appears
at
50.1°.
What
is
the
Ni
lattice
spacing,
d?
 
 
 4. Mathematical
Tools
for
Quantum
Mechanics.
 For
each
of
the
following
operators,
state
whether
it
is
linear
and
whether
it
is
 Hermitian.
Justify
your
answers.
 a Af x d dx x3 fx b Bf x d2 dx2 x fx c Cf x 0 f x' exp x2 fx d dx x' 2 d Df x e Ef x d dx x2 f x 

 ...
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