Unformatted text preview: / d x Answer: The ±rst derivatives are, [1, p. 60]: d d x sin( kx ) = k cos( kx ) d d x cos( kx ) = − k sin( kx ) so they are not eigenfunctions of d / d x . But a second diFerentiation gives: d d x p d d x sin( kx ) P = d d x ( k cos( kx )) = − k 2 sin( kx ) d d x p d d x cos( kx ) P = d d x ( − k sin( kx )) = − k 2 cos( kx ) 2.5.3 Solution eigvals-c Question: Show that sin( kx ) and cos( kx ), with k a constant, are eigenfunctions of the inversion operator Inv, which turns any function f ( x ) into f ( − x ), and ±nd the eigenvalues....
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This note was uploaded on 01/06/2012 for the course PHY 3604 taught by Professor Dr.danielarenas during the Fall '11 term at UNF.
- Fall '11