This preview shows pages 1–2. Sign up to view the full content.
Today: Review
Exam:
Tomorrow 7:30  9:15pm, MEUN E050
Topics:
All we have done so far (TZD: 17)
Allowed materials:
Two letter papersized, hand
written cheatsheets (all four sides) and a
Calculator.
But: Textbooks, cell phones, laptops, radios,
TVs, potplants, aquarium, smokes, beer, etc.
are not allowed.
What brought us to the Schröd. equ?
EMwaves
Wave equation:
Probability to
find photon:
E(x,t)
EM wave
function:
E
2
⋅
dx
De Broglie:
‘Nature is symmetric’
‘Matter is a wave’
λ
=h/p
2
2
2
2
2
1
t
E
c
x
E
∂
∂
=
∂
∂
(1D In free space)
E = hf
Energy
x
V(x)
n=1
n=2
n=3
ψ
(x)
t
t
x
i
t
x
t
x
V
x
t
x
m
∂
Ψ
∂
=
Ψ
+
∂
Ψ
∂
−
)
,
(
)
,
(
)
,
(
)
,
(
2
2
2
2
h
h
Wave equation:
Probability to
find particle:
Wave
function:
t
t
x
const
x
t
x
∂
Ψ
∂
=
∂
Ψ
∂
)
,
(
.
)
,
(
2
2
1D In free space:
Matter waves:
Ψ(x,t)
Ψ
2
dx
Vibrations on a string:
Electromagnetic waves:
Classical wave Equations
2
2
1
y
y
∂
∂
2
2
1
E
E
∂
∂
x
y
E
x
2
2
2
t
v
x
∂
=
∂
v
= speed of wave
2
2
2
t
c
x
∂
=
∂
c
= speed of light
Magnitude is nonspatial:
= Strength of Electric field
Magnitude is spatial:
= Vertical displacement of String
Solutions: E(x,t)
Solutions: y(x,t)
EM waves vs. matter waves
EM Waves (light/photons):
Amplitude E = electric field
E
2
tells us probability of
finding photon.
Maxwell’s Equations:
Matter Waves (electrons, etc.):
Amplitude
ψ
= “wave function”

Ψ

2
tells us probability of
finding particle.
Schrödinger Equation:
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 staff
 Physics, Heat

Click to edit the document details