Lecture 6

Question 1

What is probability flux, j?

Answer 1

The rate of flow of probability.
- Specifically, this is hte rate fo change in the porbability of finding a quantum particle at a particular location
- j can be the probability fflox of a single particle or a beam of particles
- As probabilitiies always sum to 1, we must appreciate that the probability flux is a conserved quantity.

Question 2

What is the continuity equation? [red]

Answer 2

partial (probability density)/partial t = - grad dot j

In one dimension this simplifies to:
partial(Psi*Psi)/partial t = - partial j(x,t)/partial x

Question 3

What is the equation for probability flux in 1 and 3 dimensions? [red]

Answer 3

j(x) = - ihbar/2m [ Psi* partial Psi/partial x - Psi partial Psi*/partial x]

j = -ihbar/2m [Psi* grad Psi - Psi grad Psi*]

Question 4

What is the probability flux of a real wavefunction?

Answer 4

0

Question 5

What is the persistance of normalisation?

Answer 5

The normalisation of a wavefunction is time-invariable. Can be shown by combining the continuity equation with the expression for probability flux which reduces to dP/dt = 0.