A free particle moving in one dimension has wave function
Ψ(x,t)=A[ei(kx−ωt)−ei(2kx−4ωt)]
where k and ω are positive real constants.
Part A
At t = 0 what are the two smallest positive values of x for which the probability function |Ψ(x,t)|2 is a maximum?
Express your answers in terms of the variable k and π. Enter your answers in ascending order separated by a comma.
Part B
At t = 2π/ω what are the two smallest positive values of x for which the probability function |Ψ(x,t)|2 is a maximum?
Express your answers in terms of the variable k and π. Enter your answers in ascending order separated by a comma.
Part C
Calculate vav as the distance the maxima have moved divided by the elapsed time.
Express your answer in terms of the variables ω and k
