# Lect08 - Labs next week NOTE You will need your Active...

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Labs next week – NOTE: You will need your “Active Directory” Login {www.ad.uiuc.edu} Note: You can save a lot of time by reading the lab ahead of time – it’s a tutorial on how to draw wavefunctions.

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Particles in Finite Potential Wells n=1 n=2 n=3 n=4 U(x) 0 L U 0 I II III U →∞ U →∞ n=0 n=1 n=2 n=3 ψ( x ) x
Overview z Particle in a finite square well potential Solving boundary conditions Comparison with infinite-well potential z Particle in a harmonic oscillator potential Electronic states in molecular potentials Vibrational states of molecules

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Example of a microscopic potential well Example of a microscopic potential well -- -- a semiconductor “quantum well” a semiconductor “quantum well” Deposit different layers of atoms on a substrate crystal: AlGaAs GaAs AlGaAs U(x) x Al As Ga Process: Molecular Beam Epitaxy Effusion cells An electron has a lower energy in GaAs than in AlGaAs. It may be trapped in the well. “Nanoscale engineering” Quantum wells like these are used for light emitting diodes and laser diodes, such as the ones used in your cd player. (The LED was developed at UIUC by Nick Holonyak)
Particle in a Box: Review U= U= ψ (x) 0 L x n=1 n=2 n=3 |ψ| 2 U= U= 0 x L U= U= 0 x L E n n=1 n=2 n=3 z We can trap a particle in a box z The probability distribution is |ψ| 2 z The energy is proportional to n 2 ) n / L 2 ( n mL 8 h m 2 h m 2 p E 2 2 2 2 2 2 n = = = = λ λ

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