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Homework Help
Advanced Physics Homework Help
Associated vs. Non-associated Laguerre Polynomials
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[QUOTE="terp.asessed, post: 4937476, member: 523168"] [h2]Homework Statement [/h2] Could someone pls clarify if the value of x changes from just Laguerre polynomial to associated one? I am confused about the role of variable x. [h2]Homework Equations[/h2] From what I have learned in the class, I understand that L[SUP]1[/SUP][SUB]n[/SUB](x) = d/dx Ln(x), n = 1, 2, 3... [h2]The Attempt at a Solution[/h2] Because L[SUB]1[/SUB](x) = 1 - x and L[SUB]2[/SUB](x) = 2 - 4x + x2 I did: L[SUB]1[/SUB][SUP]1[/SUP](x) = d/dx L1(x) = d/dx (1 - x) = -1 L[SUP]1[/SUP][SUB]2[/SUB](x) = d/dx L2(x) = d/dx (2-4x+x2) = 2x - 4 = 2(x - 2)...I wonder if x is a different function of radius in L[SUB]1[/SUB][SUP]1[/SUP](x) (as in 1s orbital) and L[SUP]1[/SUP][SUB]2[/SUB](x) (as in 2s orbital)? I am assuming the orbital polynomial on the basis of node...as in: L[SUB]1[/SUB][SUP]1[/SUP](x)= 1 because of 0 nodes...hence 1s L[SUP]1[/SUP][SUB]2[/SUB](x) = 2x -4 because of 1 node...hence 2s [/QUOTE]
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Associated vs. Non-associated Laguerre Polynomials
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