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Physics 222
Physics 222
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Physics 222
Two
Important Properties of Waves
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%;top:.49em'>n Not
localized
<=
span
style=3D'visibility:hidden'>n
n Great=
er
localization in space implies poorer localization in
wavelength
<=
span
style=3D'visibility:hidden'>n
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Physics 222
Quiz Que=
stion
n If ψ is the wavefunction of a particle, where am I most likely to find the particle?
n A:
Where ψ is the largest. <=
span
style=3D'font-size:113%;display:none'>
n B:
Where ψ is the smallest. =
n C:
Where ψ 2 is the largest.
n D:
Where | ψ | 2 is the largest.
n E:
It has nothing to do with ψ .
<=
span
style=3D'font-size:113%;visibility:hidden'>n
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Physics 222
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Physics 222
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Physics 222
No you feeble minded rodent, why is ª <=
/span>not defined such that ª and not | ª | <=
span
style=3D'font-size:55%;position:relative;top:-.45em;mso-text-raise:30%'>2<=
/span> is <=
/span>proportional to probability of finding the particle? =
Are you
pondering
what
I’m pondering?
Yeah, but=
I
don’t think
snails li=
ke
yodeling.
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dOn/2e==
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Physics 222
Thought
Question
n What tells us about the probability of finding a p=
hoton
at a particular
location?
n A: T=
he
electric field
n B: T=
he
magnetic field
n C: T=
he
intensity
n D: T=
he wave
vector
n E: T=
he
Poynting vector
n
Physics 222
What else does the
photon’s wave function tell us?
n The Poynting vector (ExB) tells us=
the
direction it is going.
<=
span
style=3D'visibility:hidden'>n
<=
span
class=3DBB style=3D'position:absolute;left:-4.43%;top:.49em'>n The e=
lectric
field tells us how it will interfere.
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Physics 222
What do Quantum Waves =
Represent?
n Everything about=
the
object’s state
<=
span
class=3DB1B style=3D'position:absolute;left:-3.43%;top:.49em'>n Posi=
tion,
momentum, angular momentum, excitation energy, dipole moment,
etc.
<=
span
class=3DBB style=3D'position:absolute;left:-3.8%;top:.49em'>n Does it
express the object’s temperature?
n What does the
amplitude represent?
<=
span
class=3DBB style=3D'position:absolute;left:-4.19%;top:.49em'>n Are t=
here
other ways to represent the wave function?
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Physics 222
Quantum Probability –=
=
Ensemble
Average
<=
span
class=3DBB style=3D'position:absolute;left:-4.14%;top:.49em'>n Start=
with a
million copies of the same wavefunction.
<=
span
class=3DBB style=3D'position:absolute;left:-4.22%;top:.49em'>n Measu=
re the
location of each particle.
n Generate a
Histogram
n ª *<=
/span>ª
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Physics 222
Quiz Que=
stion
n Why did Davison and Germer heat=
their
nickel target?
n
n A – To induce thermal emi=
ssion
of electrons
=
n B – To remove oxide contamination
n C – To study the thermal
expansion coefficient of pure nickel
n D – To produce blackbody
radiation
n E – To keep the=
ir
graduate students from sitting on it (ouch, that’s hot!)
Physics 222
P (x ,t )/ E2
Photon with well
defined wavelength:
E E =
0=
sin( kx - ! t )
Red=3D<=
/span>E ( x , t )
<=
/span>
Blue=
=3D P ( x , t )
Physics 222
P (x ,t )/ &o=
rdf; *<=
/span>ª
Electron in free=
space
with well defined wavelength:
ª =3D Ae <=
i>i (=
kx - ! t =
)=
Red=3D=
Re[ ª ( x ,t )]
Gr=
een=3DIm[ ª (x , t )]
Blue=
=3D P ( x , t )
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