Particle penetrating a barrier. Suppose a particle of energy E impinges on a step potential: V (x) = 0 for x V0 for x0 , where V0 E . Show that, in the classically forbidden region, an exponentially decaying wavefunction of the form: ψ (x)= Aexp[-κx] satisfies the time- independent Schrödinger equation and write down the appropriate expression for κ in terms of E, V0, and m. Don’t worry about the normalization constant A.

Question

Particle penetrating a barrier. Suppose a particle of energy E impinges on a step potential:
V (x) = 0 for x < 0 and V=(x) >V0 for x>0 , where V0 > E . Show that, in the classically forbidden region, an exponentially decaying wavefunction of the form: ψ (x)= Aexp[-κx] satisfies the time-
independent Schrödinger equation and write down the appropriate expression for κ in terms of E, V0, and m. Don’t worry about the normalization constant A.