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The functions of interest in hydrogen atom theory are: 1+1 -2 21+1, f₁(x) = x¹+¹ e "L (+) n-1-1 In Eqn 2.1, n and I are integers and 0 ≤ 1 ≤ n - 1. For l = 1, show that: ²e + Note: L n-1-1 1 2- f,(x) = gx e 21+1 k is the Associated Laguerre Polynomial, L

The functions of interest in hydrogen atom theory are: 1+1 -2 21+1, f₁(x) = x¹+¹ e "L (+) n-1-1 In Eqn 2.1, n and I are integers and 0 ≤ 1 ≤ n - 1. For l = 1, show that: ²e + Note: L n-1-1 1 2- f,(x) = gx e 21+1 k is the Associated Laguerre Polynomial, L

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The functions of interest in hydrogen atom theory are: x 1+1 2n f(x) = x e L 21+1(±) n-1-1 In Eqn 2.1, n and I are integers and 0 ≤ 1 ≤ n - 1. For l = 1, show that: 2 f₂(x) = = x ²e + 8 Note: L n-l-1 21+1 is the Associated Laguerre Polynomial, L p (2.1) (2.2)
Transcribed Image Text:The functions of interest in hydrogen atom theory are: x 1+1 2n f(x) = x e L 21+1(±) n-1-1 In Eqn 2.1, n and I are integers and 0 ≤ 1 ≤ n - 1. For l = 1, show that: 2 f₂(x) = = x ²e + 8 Note: L n-l-1 21+1 is the Associated Laguerre Polynomial, L p (2.1) (2.2)
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