A particle trapped in a potential has the following wavefunction: Ψ(x,t)=Ae−λ∣ˣ∣ e−ᶦωᵗ. where A,λ, and ω are positive-valued parameters.

(a) Normalise the wave function.
(b) Plot the probability density P(x,t) of the particle using your own unique choice of values for the three parameters. Label your plots correctly and indicate values used.
(c)What is the particle's mean position?
(d)What is the uncertainty in the particle's position?