In the Previous Problem, If We Also Require That $\Theta$ Be Bounded Everywhere, the Solution of the Eigenvalue Problem Is

question 7

Multiple Choice

In the previous problem, if we also require that $\Theta$ be bounded everywhere, the solution of the eigenvalue problem is

• A) \(\lambda = n ( n + 1 ) , \Theta = P _ { n } ( \sin \theta ) , n = 1,2,3 , \ldots\)
• B) \(\lambda = n ( n - 1 ) , \Theta = \sin ( n \theta ) , n = 1,2,3 , \ldots\)
• C) \(\lambda = n ( n - 1 ) , \Theta = \cos ( n \theta ) , n = 1,2,3 , \ldots\)
• D) \(\lambda = n ( n + 1 ) , \Theta = P _ { n } ( \cos \theta ) , n = 1,2,3 , \ldots\)
• E) \(\lambda = n ( n - 1 ) , \Theta = P _ { n } ( \sin \theta ) , n = 1,2,3 , \ldots\)

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