Quantum Mechanics - Eigenfunction

Which of the following is an eigenfunction of the linear momentum operator −iħ ∂/∂x with a positive eigenvalue ħk; i.e., an eigenfunction that describes a particle that is moving in free space in the direction of positive x with a precise value of linear momentum?

A. cos kx
B. sin kx
C. e^−ikx
D. e^ikx
E. e^−kx

(GR8677 #57)

Solution:

Eigenequation:




(A) FALSE
cos kx → ∂(cos kx)/∂x = sin kx

(B) FALSE
sin kx → ∂(sin kx)/∂x = cos kx 

(C) FALSE
e^−ikx → ∂(e^−ikx)/∂x = −ik e^−ikx 

(D) TRUE
e^ikx → ∂(e^ikx)/∂x = ik e^ikx 

(E) FALSE
e^−kx → ∂(e^kx)/∂x = k e^kx

Answer: D