Lect07 - 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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History History "Erwin wrote to 'an old girlfriend in Vienna' to join him in Arosa .... Efforts to establish the identity of this woman have so far been unsuccessful, since Erwin's personal diary for 1925 has disappeared .... Whoever may have been his inspiration, the increase in Erwin's powers was dramatic.“ --W. Moore, Schr ö dinger [Debye said to Schrödinger in 1925 that]…to deal properly with waves, one had to have a wave equation. It sounded quite trivial and did not seem to make a great impression, but Schrödinger evidently thought a bit more about the idea afterwards. Just a few weeks later he gave a talk at the colloquium which he started by saying: "My colleague Debye suggested that one should have a wave equation; well, I have found one!" (Felix Bloch's eyewitness account Physics Today 28:12, 23–27 [1976])
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Schrödinger’s Equation and the Particle in a Box U= ψ (x) 0 L U= n=1 n=2 x n=3 Nice descriptions in the text – Chapter 40
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Overview Overview z Particle in a “Box” -- matter waves in an infinite square well z Wavefunction normalization z General properties of bound-state wavefunctions
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z Notice that if U(x) = constant , this equation has the simple form: ) x ( C dx d 2 2 ψ = ψ For positive C , what is the form of the solution? For negative C , what is the form of the solution? where is a constant that might be positive or negative. ) E U ( 2m C 2 = = a) sin kx b) cos kx c) e ax d) e -ax a) sin kx b) cos kx c) e ax d) e -ax KE term PE term Total E term ) ( ) ( ) ( ) ( 2 2 2 2 x E x x U dx x d m ψ ψ ψ = + = Last lecture: The time-independent SEQ (in 1D)
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z Notice that if U(x) = constant , this equation has the simple form: ) x ( C dx d 2 2 ψ = ψ For positive C , what is the form of the solution? For negative C , what is the form of the solution? where is a constant that might be positive or negative. ) E U ( 2m C 2 = = a) sin kx b) cos kx c) e ax d) e -ax a) sin kx b) cos kx c) e ax d) e -ax KE term PE term Total E term ) ( ) ( ) ( ) ( 2 2 2 2 x E x x U dx x d m ψ ψ ψ = + = Last lecture: The time-independent SEQ (in 1D)
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Particle in a Box Particle in a Box z The solution of the Schrodinger Eq. discussed today is NOT mysterious!
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