Question

Circle each of the three listed functions that is an eigenfunction of the specified operator For each eigenfunction, write the eigenvalue below the function.

Answer 1

is L is the operator, and v is the function and x is the eigen value, then

Lv=xv.

a) We can see than

if v=e^(-kx),

Lv=-ke^(-kx)=-kx

so, x=-k

so the eigen value is -k

b)for cos(kx) function,

L2v=-k^2cos(kx)=-k^2v

so the eigen value is -k^2

if v=e^-kx,

L2v=k^2e^(-kx)

so, x=k^2

so the eigen value is k^2