course | course_year | question_number | tags | title | year | |||
---|---|---|---|---|---|---|---|---|
Methods |
IB |
50 |
|
Paper 1, Section II, A |
2016 |
(a) Consider the general self-adjoint problem for
where
(b) Consider the problem for
(i) Recast this problem into self-adjoint form.
(ii) Calculate the complete set of eigenfunctions and associated eigenvalues for this problem. [Hint: You may find it useful to make the substitution
(iii) Verify that the eigenfunctions associated with distinct eigenvalues are indeed orthogonal.