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385lec25 - PHYS 385 Lecture 25 Hydrogen atom II Lecture 25...

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PHYS 385 Lecture 25 - Hydrogen atom - II 25 - 1 ©2003 by David Boal, Simon Fraser University. All rights reserved; further copying or resale is strictly prohibited. Lecture 25 - Hydrogen atom - II What's important : solution of the radial equation form of the wavefunctions Text : Gasiorowicz, Chap. 12 At the end of the previous lecture, we had reduced the radial part of the Schrödinger equation into solving the equation L" + {2( l +1) - ] L' + ( - l - 1) L = 0 (1) where L has the series expansion L = a o + a i 1 + a 2 2 + . .. The solution method is the same as that for the Hermite polynomials in the harmonic oscillator: one finds a recursion relation between successive coefficients and demands that the series be truncated at some finite a k . Collecting terms multiplying k from (1) gives: k-1 ( k +1) k a k+1 k 2( l +1)( k +1) a k+1 - k-1 k a k k ( - l - 1) a k so ( k +1) k a k+1 + 2( l +1)( k +1) a k+1 - k a k + ( - l - 1) a k = 0 or [( k +1) k + 2( l +1)( k +1)] a k+1 + [ - l - 1 - k ] a k = 0 or
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385lec25 - PHYS 385 Lecture 25 Hydrogen atom II Lecture 25...

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