{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hwk7 - z very close to-1 Show that the solutions are...

This preview shows page 1. Sign up to view the full content.

Physics 604 Homework #7 Fall ‘11 Dr. Drake 1. The Coulomb Wave equation is given by d 2 w dz 2 + " 1 - 2 η z - L ( L + 1) z 2 # w = 0 (a) Classify the singular points of this equation. (b) Find the behavior of the solutions for z very close to zero. Show that the solutions are linearly independent. Are there special cases where they are not linearly independent? What are the solutions in this case? 2. The Legendre equation is given by (1 - z 2 ) d 2 w dz 2 - 2 z dw dz + α ( α + 1) w = 0 . (a) Classify the singular points of this equation. (b) Find the behavior of the solutions for
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: z very close to-1. Show that the solutions are linearly independent. (c) Calculate the full series solution around z =-1. Note: this is a degenerate case. 3. Bessel’s equation is given by z 2 d 2 w dz 2 + z dw dz + ( z 2-ν 2 ) w = 0 . (a) Identify the location of the singular points of this equation. (b) Find the lowest order behavior of the solution around z = 0. What is the behavior if ν = 0....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online