Transcript T3_Static_Potentials_And_Eigenstates

Static Potentials and
Eigenstates
Classical Particle in a Box
Quantum Particle in a Box:
The Infinite Square Well
Particle in an Infinite Square Well:
The Wavefunction  The Probability Density
The Harmonic Oscillator Potential
The Harmonic Oscillator Energy Levels
The Harmonic Oscillator Wavefunctions
for the First Four Energy Levels
The Harmonic Oscillator Probability Densities
for the First Four Energy Levels
The Harmonic Oscillator Probability Density
and the Approach to Classical Behavior for Large n
Local Minima in Complicated Potentials
May Be Approximated as Harmonic Oscillators
Particle From the Left Tunneling Through a
Potential Barrier
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Matter as a Wave
• Originally postulated by de Broglie in 1924
– NO evidence at this point
– He surmised that l=h/p: E=1/2 mv2=p2/2m
• Davison-Germer (1924)
– Electron diffraction
– Found by accident (“faulty” nickel target)
– “ruined” Germer’s second honeymoon
• G.P. Thompson – Went through the crystal
Light as a Particle
•Light of very low intensity – can see
single “particles” that DO have
momentum hit screen
•Eventually the expected double slit
diffraction pattern emerges
•Light consists of photons (massless
particles) – originally postulated by
Einstein
•Ephoton=hf=hc/l
•h=6.63x10-34 Js (Planck’s constant)
Particle Waves
ln=2L/n
Since l=h/mv,
vn=nv1
v1=h/(2Lm)
En=½mvn2
En=n2E1
E1=h2/(8mL2)
Me: l=10-34 m, E1=10-38 J,
n=1035 (n BIG, classical)
Electrons not!!!
Spectrometer
The end of the 19th century
– towards the slow death of
classical physics
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