ECE440_Carney_L8

Zaonfromthebox notduetothelapce volumekspaceperstate

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Unformatted text preview: mass
 •  They’re
s?ll
described
by
QM,
so
we
need
a
 pathway
to
“freedom”

 •  Start
by
puPng
the
p’cle
in
a
bow
and
take
the
 large
box
limit
 2π nx kx = Lx 2π ny ky = Ly 2π nz kz = Lz Momentum
states
 in
a
finite
volume
 Lz The
box
 Ly Quana?za?on
from
the
box,
 NOT
due
to
the
laPce
 Volume
(k‐space)
per
state:
 ⎛ 2π ⎞ ⎛ 2π ⎞ ⎛ 2π ⎞ 8π 3 Vk = ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ = Vr ⎝ L x ⎠ ⎝ L y ⎠ ⎝ Lz ⎠ Lx ky kx quan?za?on
volume
(coordinate
space)
 More
states
in
momentum
space
 Vr 3 dnk = V d k = dk 3 8π −1 k 3 differen?al
number
...
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