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.

Question

Mathematics

Davis Hodge

26 April, 15:50

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.

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Hull · 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