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Unformatted text preview: 3/9/11 1 1 PHYS 360 Quantum Mechanics Wed Mar 9, 2011 Lecture 24: Finally, the hydrogen atom. Did Bohr get anything right? The Hydrogen Atom First, lets consider the Bohr model. This was before quantum mechanics, but it did assume quanpzapon. 1. Classical electron orbits, circular, but with quanpzed angular momentum: mvr = n 2. Transipons between orbits leads to emission of a hoton: E = = E n E m Note: there are NO wave funcpons. Then insert Coulomb force into Newtons 2 nd law: F = ma = mv 2 r = Ze 2 r 2 2 Note: much of Bohrs original argument was based on the Corresondence Princile. Also note: Aer the de Broglie hyothesis was made (that =h/), it was found that quanpzed angular momentum meant an integer number of wave lengths er orbit. 3 The Bohr Model Predicpons: Ground state binding energy E = 1 2 mc 2 ( Z ) 2 = 13.6 eV Bohr radius a o = mc 0.529 10 10 m This was sucient to rovide good agreement with all of the known sectroscoic data at that pme. e 2 c 1 137 fine structure constant 4 Back to QM in three dimensions.. 5 6 i ( r , t ) t = 2 2 m 2 ( r , t ) + V ( r , t ) ( r , t ) n r , t ( ) = n ( r ) e iE n t / 2 2 m 2 + V = E ( r , , ) = R ( r ) Y ( , ) = R ( r ) ( ) ( ) 1 R d dr r 2 dR dr 2 mr 2 2 V ( r ) E = l l + 1 ( ) The Radial Equapon: 1 sin d sin...
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This note was uploaded on 04/23/2011 for the course PHYS 360 taught by Professor Durbin,stephen during the Spring '11 term at Purdue UniversityWest Lafayette.
 Spring '11
 DURBIN,STEPHEN
 Orbits

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