PHYS 445 Lecture 5  Fundamental postulate
5  1
© 2001 by David Boal, Simon Fraser University.
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Lecture 5  Fundamental postulate
What's Important:
•
description of a state
•
probability
•
density of states
Text
: Reif
Secs. 2.1 to 2.5 should be read independently
Description of a state
In
classical mechanics
, a 3D system of
N
particles without spin or any internal structure
can be described by 6
N
variables.
positions:
q
1
...
q
N
(coordinates are the degrees of freedom)
momenta:
p
1
...
p
N
Knowing these quantities at a particular time, one can use Hamilton's or Newton's
equations to predict their values at all later times.
The coordinate variables
q
are
called the degrees of freedom
f
of the system.
Here, there are 3
N
coordinates so
f
=
3
N
.
The positions and momenta of the particles form the
phase space
of the system.
In
spin systems
on a fixed lattice, the degrees of freedom are the spin orientations:
↑↓↓↑↑↑↓↓↓↑↑↓↑↓↑↑
f
degrees of freedom
In quantum mechanics, the number of degrees of freedom is the number of quantum
numbers required to specify the state.
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 Spring '08
 DavidBoal
 Physics, mechanics, Energy, Fundamental physics concepts, fundamental postulate, David Boal

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