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Lecture_14 - PHYS PHYS342 Fall2011 Lecture Lecture 14...

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PHYS 342 Fall 2011 Lecture 14: Schrödinger’s Equation Schrödinger s Equation in 3 dimensions – Atomic Hydrogen Ron Reifenberger Bi k N t h l C t Birck Nanotechnology Center Purdue University Lecture 14 1
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What we’d like to know 1. Does the Schrödinger equation reproduce Bohr’s theory from 1913? Only certain allowed electron orbits? Quantized radius for each orbit? Quantized angular momentum? d Quantized energy states? Discrete emission lines? 2. What really is going on during the light emission process inside an atom? 3. What is the electronic structure of other atoms in the periodic table? 2
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What we’ve learned so far Commonly observed objects Particle Wave Box Box Tightly confined objects with small mass ?? 3 No compelling reason to expect such objects to fit into these two boxes!
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What is the hydrogen atom? One electron bound to one proton What is U(r) for the hydrogen atom? e r m 1840 m +e -e m e p e 2 1 2 1 1 ( , , ) ( ) 4 4 o o q q e U x y z U r r r     electrostatics U(r) C t l F r 4 Central Force means U(x,y,z) = U(r)
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