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Introduction to Quantum Mechanics How to solve for P(2) to P(5)?

Introduction to Quantum Mechanics How to solve for P(2) to P(5)?

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Introduction to Quantum Mechanics How to solve for P(2) to P(5)?
Po=1 P₁ = x P₂ = 1/2 (3x²-1) P3=-1-(5x³-3x) P4=(35x² 30x²+3) P₁= -(63x³-70x³+15x) P5
Transcribed Image Text:Po=1 P₁ = x P₂ = 1/2 (3x²-1) P3=-1-(5x³-3x) P4=(35x² 30x²+3) P₁= -(63x³-70x³+15x) P5
and P(x) is the lth Legendre polynomial, defined by the Rodrigues formula: l 1 d 2/²0 (1) ² (x² - 1) ². 2⁰ l! dx For example, Pe(x) = Po(x) = 1, P₁(x)= d = 1 / ² (x² - 1) = x₁ 2 dx 2 1 d 1 12.00 - (-)² (2²-1)² - (32²-1) (x) = = 1/2 4.2 dx (4.28)
Transcribed Image Text:and P(x) is the lth Legendre polynomial, defined by the Rodrigues formula: l 1 d 2/²0 (1) ² (x² - 1) ². 2⁰ l! dx For example, Pe(x) = Po(x) = 1, P₁(x)= d = 1 / ² (x² - 1) = x₁ 2 dx 2 1 d 1 12.00 - (-)² (2²-1)² - (32²-1) (x) = = 1/2 4.2 dx (4.28)
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