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MSE 2020
1/25/2011
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Electrons
•
An electron is a charged particle, so changing its motion is easy using electric and
magnetic fields
o
Ex. Harmonic oscillation
mv22
+
= (
)
kx22 E macroscopic
=
(
)
H harmonic operator Hamiltonian
H
=
→
Ψ EΨ Schrodinger Equation

+
ħ22mδδx
Ux
=
E
o
Particle in a Box
•
The electron wave must be at 0 at the ends of the box
o
What is the largest wave possible?
o
λ = 2L
o
What are possible wavelengths?
o
λ
= L, 3λ/2 = L,…, λ = 2L/n, where n = 1,2,3,…
o
•
The wavelength depends on the size of the box
•
Use the De Broglie equation
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1/25/2011
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o
=
p
hλ
o
=
=
E
p22m
n2h28mL2
(discrete energy levels/values because n = 1, 2,3,
…)
o
Discrete wavelengths and energy
•
This occurs because the electron is confined to the atom
•
Schrodinger equation has only been solved for the H atom
o
o
Quantum Numbers
•
Principal quantum number: n, n=1 (for H atom)
•
Angular momentum quantum number: l = 0,1,.
.., n1
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This note was uploaded on 09/12/2011 for the course MSE 2020 taught by Professor Alamgir during the Spring '09 term at Georgia Institute of Technology.
 Spring '09
 ALAMGIR

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