Question

A three dimensional wavefunction of a parrticle is (r) = c/e exp(-kr/i). calculate the probability current density

Answer 1

To calculate the probability current density, we need to find the derivative of the wavefunction and multiply it by the complex conjugate of the wavefunction.

Step-by-step explanation:

To calculate the probability current density, we need to find the derivative of the wavefunction with respect to the radial coordinate r, and then multiply it by the complex conjugate of the wavefunction:

J(r) = -i / 2m (ψ*(r) ∇ ψ(r) - ψ(r) ∇ ψ*(r))

In this case, the wavefunction is given by (r) = c/e exp(-kr/i), so we can substitute this into the formula and simplify to find the probability current density.