Biomedical Engineering Reference
In-Depth Information
that.location..his.subtle.distinction.emphasizes.the.point.that.interference.is.a.single.photon.phenom-
enon.and.is.not.caused.by.interactions.of.photons.
Photons.interact.exclusively.with.charged.particles,.most.oten.with.electrons..In.fact,.almost.every-
thing.we.know.about.the.world.is.transmitted.to.us.through.the.photon-electron.interaction..For.exam-
ple,.heat.in.the.sun.or.a.lightbulb.excites.electrons,.which.when.accelerated.emit.electromagnetic.waves.
(photons).. he. photons. either. relect. of. of. surfaces. or. interact. with. electrons. on. the. surface. which.
absorbs.and.reemits.photons..Finally,.the.photons.are.detected.in.the.eye..he.photon.moves.an.electron.
on.the.retina's.detectors.to.a.higher.energy.state..his.produces.an.electrical.signal,.which.is.then.trans-
mitted.to.the.brain.
When.a.photon.interacts.with.a.charged.particle,.the.process.can.be.explained.as.a.scattering.phe-
nomenon. known. as. Compton. scattering. (Figure. 1.9).. his. is. consistent. with. a. classical. explanation.
where. the. electromagnetic. wave. exerts. force. on. the. electron,. making. the. electron. accelerate,. which.
then.results.in.a.new.electromagnetic.wave.(a.moving.charge.is.a.source.term.in.Maxwell's.equations).
superposing. intensity. with. the. irst.. Quantum. mechanically,. a. photon. collides. with. an. electron. and.
exchanges. energy. and. momentum. with. it.. he. photon. scatters. with. a. diferent. wavelength. (diferent.
energy.and.momentum),.which.mixes.with.all.the.other.photons.that.missed.the.electron.
Electromagnetic. radiation. carries. energy. and. momentum. density. in. its. ields.. Classically,. the. ield.
energy.density.is.a.function.of.the.magnitude.of.the.
E
.and.
B
.ields:
1
8
E
1
4
ˆ
.
∫
EM
∫
E
=
(
E
2
+
B
2
) d
V
p
=
k
=
(
E B
×
) d
V
EM
π
c
π
c
EM
Under.the.quantum.mechanical.explanation,.each.photon.individually.has.energy.and.momentum:
E
c
ˆ
.
ph
E
=
hv
p
=
k
=
k
ph
ph
=
c n
.is.the.frequency.of.the.light,.and.
k
.is.the.vector.wavenum-
ber.with.magnitude.2π/λ.and.direction.pointing.in.the.direction.of.photon.motion.
We.explored.earlier.how.difraction.is.a.consequence.of.wave.phenomena..When.an.incident.wave.
is. conined. to. pass. through. an. opening,. there. are. additional. components. in. the. resulting. wave. that.
difract. away. from. the. nominal. direction. of. the. original. wave.. Although. difraction. is. not. an. obvi-
ous.consequence.of.particle.motions,.difraction.of.particles.can.be.explained.quantum.mechanically,.
through.the.Heisenberg.uncertainty.principle,.with.the.same.resulting.difraction.as.the.wave.theory..
he. uncertainty. principle. of. Heisenberg. states. that. the. energy. and. momentum. cannot. be. simultane-
ously.determined.to.ininite.accuracy..Instead,.the.product.of.the.uncertainties.has.a.minimum.value..
In.the.case.of.the.photon,
where.
h
.is.Plank's.constant,.
ℏ
.=.2π/
h
,.
ν
λ
.
∆
x p h
≅
E
e
-
k
B
e
-
ph
m
‥
=
q
[
E
+
v
/
c
)
×
B
]
- — ⏤
․‥
2
e
2
c
3
λ' - λ=
2
h
mc
θ
2
sin
2
.
.
3
FIGuRE 1.9
Compton.scattering.explained.by.classical.electromagnetism.(EM).(
let
).or.by.quantum.mechanics.
(
right
).
