Lect08 - Introduction to Quantum Mechanics This week (and...

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Introduction to Quantum Mechanics This week (and the previous week) are critical for the course Week 4 – Lect. 7,8: Schrödinger Equation -- Definite predictions of quantum behavior -- Examples of particles in infinite wells, finite wells -- Leads up to rest of course Lab next week -- You will need your “Active Directory” Login {www.ad.uiuc.edu} -- You can save a lot of time by reading the lab ahead of time – it’s a tutorial on how to draw wavefunctions Midterm Exam – Monday, Feb. 11 - will cover Lectures 1-7 and qualitative aspects of lecture 8 Week 4 – Discussion and quiz will be on material in lect. 5-6 Week 4 – Online homework covers material in lects. 7-8. It is due 8 AM Thurs. Feb. 14, but we strongly encourage you to look at the homework before the midterm! Practice Exams – Additional problems on Lect. 7,8 material Review – Sunday, Feb. 10, 3-5pm Lincoln Hall Theater, Spr06 Extra office hours Feb. 10 and 11 (also Feb. 13, for the HW)
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“All of modern physics is governed by that magnificent and thoroughly confusing discipline called quantum mechanics. ..It has survived all tests and there is no reason to believe that there is any flaw in it….We all know how to use it and how to apply it to problems; and so we have learned to live with the fact that nobody can understand it.” --Murray Gell-Mann
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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
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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” Nanoscale Nanoscale Engineering” Engineering” Deposit different layers of atoms on a substrate crystal: AlGaAs GaAs AlGaAs U(x) x Al As Ga An electron has a lower energy in GaAs than in AlGaAs. It may be trapped in the well – but it “leaks into the surrounding region to some extent Effusion cells Process: Molecular Beam Epitaxy Quantum wells like these are used for light emitting diodes and laser diodes, such as the ones used in your cd player. ( Note: The LED was developed at UIUC by Nick Holonyak)
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Particle in a Box: Review 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 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
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Particle in a Finite Well (1) z What if the walls of our “box” aren’t infinitely high? “Finite Square Well” and E < U 0 Introduces very important concept of “barrier penetration” z Need to solve SEQ in 3 regions: Region II: Same as infinite square well: U(x) = 0 0 ) ( ) ( 2 ) ( 2 2 2 = + x U E m dx x d ψ = U(x) 0 L U 0 I II III E The general solution to the SEQ in this region is: kx cos B kx sin B ) x ( 2 1 II + = E m 2 2 k
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This note was uploaded on 09/12/2009 for the course PHYS 214 taught by Professor Debevec during the Spring '07 term at University of Illinois at Urbana–Champaign.

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Lect08 - Introduction to Quantum Mechanics This week (and...

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