Question

Identify which of the following functions are eigenfunctions of the operator d/dx: (a) eikx, (b) cos kx, (c) k, (d) kx, (e) e−ax2 . Give the corresponding eigenvalue where appropriate.

Answer 1

Answer: Identify which of the following functions are eigenfunctions of the operator d/dx: (a) eikx, (b) cos kx, (c) k, (d) kx, (e) e−ax2

Step-by-step explanation: First, we going to apply the operator derivate to each item. Remember that  a function f is an eigenfunction of D if it satisfies the equation

Df=λf, where  λ is a scalar.

a) D(eikx)/dx= ik*eikx, then the function is a eigenfunction and the eingenvalue is ik.

b) D(cos kx)/dx= -ksen kx, then the funcion is not a eigenfunction.

c)  D(k)/dx=0, then the funcion is not a eigenfunction.

d)  D(kx)/dx=k, then the funcion is not a eigenfunction.

e)  D(e-ax2)/dx= -2ax*e-ax2, then the function is a eigenfunction and the eingenvalue is -2ax