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

Question

Alex Ar [27]

4 years ago

11

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

2 . Give the corresponding eigenvalue where appropriate.

Mathematics

1 answer:

grigory [225] · Answer 1 · 2022-01-03T10:14:55+03:00

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