Physics 344
Foundations of 21
st
Century Physics:
Relativity, Quantum Mechanics and
Their Applications
Their Applications
Instructor:
Dr. Mark Haugan
Office:
PHYS 282
[email protected]
TA:
Dan Hartzler
Office:
PHYS 7
[email protected]
Grader:
Shuo Liu
Office:
PHYS 283
[email protected]
Office Hours:
If you have questions, just email us to make an
appointment
We enjoy talking about physics!
appointment.
Reading:
Chapter 3 of the text.
Notices:
Graded homework will be returned on Tuesdays during the
help session in PHYS 160 from 1:30 to 3:30.

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Recitation Recap
A way to use vectors to understand and work with
ˆ
y
ˆ
y
′
transformations between inertial coordinate systems.
The figure shows the unit vectors pointing
in the direction of the
x
and
y
axes of one
ˆ
sin( )
x
θ
−
θ
ˆ
x
′
in the direction of the
and
axes of one
coordinate system and the x’ and y’ axes
of another one rotated relative to the
first one about their common
z
,
z’
axis.
1
ˆ
1
ˆ
cos( )
y
θ
θ
ˆ
x
Since the unit vectors of the primed system
ˆ
cos( )
x
θ
sin( )
y
θ
ˆ
ˆ
ˆ
cos( )
sin( )
x
x
y
θ
θ
′
=
+
Since the unit vectors of the primed system
are vectors, we can represent them as
a sum of vectors in the directions of the
unprimed unit vectors.
ˆ
ˆ
ˆ
sin( )
cos( )
y
x
y
θ
θ
′
= −
+
ˆ
ˆ
z
z
′
=
Knowing the relationship between the sets of unit (basis) vectors allows us to
transform the coordinates of any vector!
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
(cos( )
sin( ) )
'(
sin( )
cos( ) )
'
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
(
cos( )
sin( ))
( 'sin( )
cos( ))
'
r
x x
y y
z z
x
x
y
y
x
y
z z
x
y
x
x
y
y
z z
xx
yy
zz
θ
θ
θ
θ
θ
θ
θ
θ
′ ′
′ ′
′ ′
′
=
+
+
=
+
+
−
+
+
′
′
′
+
+
+
≡
+
+
G
=
−
From this we simply read off the transformation equations.
cos( )
sin( )
'sin( )
cos( )
'
x
x
y
y
x
y
z
z
θ
θ
θ
θ
′
′
′
=
−
=
+
=