385lec24 - PHYS 385 Lecture 24 - Hydrogen atom - I Lecture...

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PHYS 385 Lecture 24 - Hydrogen atom - I 24 - 1 ©2003 by David Boal, Simon Fraser University. All rights reserved; further copying or resale is strictly prohibited. Lecture 24 - Hydrogen atom - I What's important : radial SE square well in 3D Coulomb potential Text : Gasiorowicz, Chap. 12 Radial component of Schrödinger equation A comment on the radial SE before we start. After separating out the angular components, the radial equation looks like: 1 r 2 d dr r 2 dR ( r ) dr + 2 m h 2 E - V ( r ) + h 2 l ( l + 1) 2 mr 2 R ( r ) = 0, (1) where the function that we are seeking is R ( r ). A comment on the term added to the potential energy V ( r ). This is sometimes referred to as the angular momentum barrier or "centrifugal potential barrier". As derived in PHYS 211, it originates from the angular kinetic energy V ang = I 2 /2 = ( I ) 2 / 2 I = L 2 / 2 mr 2 = l ( l +1) h 2 / 2 mr 2 . (2) The effect of this term is to push the effective potential to larger values of r . It's a real effect, in that it results from the angular part of the solution Y ( , ).
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This note was uploaded on 09/07/2009 for the course PHYS 385 taught by Professor Davidboal during the Spring '09 term at Simon Fraser.

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385lec24 - PHYS 385 Lecture 24 - Hydrogen atom - I Lecture...

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