Quantum Mechanics - Probability Current Density

A particle of mass m has the wave function 

ψ(x,t) = e^iωt [αcos(kx) + βsin(kx)] 

where α and β are complex constant and ω and k are real constants. The probability current density is equal to which of the following? (Note: α* denotes complex conjugates of α, and |α|²= α*α .)

(GR9677 #97)

Solution:

Probability density function:

Answer: E