please do parts a-c! 2. Consider the plane wave function of a free particle of mass m and characterized by positiveconstant koy(x, t) = exp[i kox-ih² ko²t/2m](a) Find its momentum space wave function (Fourier transform) Þ(k, t) in terms of a deltafunction.+ ∞{ 2π 8(a) = exp[ia b] db }- 00(b) Find the probability current J(x, t) = (i ħ / 2m) [ y (@y*/@x) — ¥*(@y/@x) ], simplifying theexpression as much as possible.D(c) If the particle entered a region with constant potential Vo> ko2/2m, what would itswave function in this region become?

2. Consider the plane wave function of a free particle of mass m and characterized by positive constant ko y(x, t)= exp [ i ko x-ih² ko²t/2m] (a) Find its momentum space wave function (Fourier transform) (k, t) in terms of a delta function. + ∞0 { 2 nd(a) = exp [ia b] db } - 00 (b) Find the probability current J(x, t) = (i ħ/2m) [y (@y*/əx) − y*(@y/dx)], simplifying the

2. Consider the plane wave function of a free particle of mass m and characterized by positive constant ko y(x, t)= exp [ i ko x-ih² ko²t/2m] (a) Find its momentum space wave function (Fourier transform) (k, t) in terms of a delta function. + ∞0 { 2 nd(a) = exp [ia b] db } - 00 (b) Find the probability current J(x, t) = (i ħ/2m) [y (@y/əx) − y(@y/dx)], simplifying the