I have been studying potential steps and barriers as well as reflection and transmission coefficients and how to derive them. Most of it makes sense to me except for one thing: As we know, the normal Schrodinger equation is: (-ħ2/2m) (∂2Ψ/∂x2) + v(x)Ψ = EΨ For a step potential however, my book and web resource both say that for the boundary conditions: v(x)= 0 for x < 0 and V0 for x ≥ 0 the Schrodinger equations are: (∂2Ψ1/∂x2) + K12Ψ1(x) = 0 and (∂2Ψ2/∂x2) + K22Ψ2(x) = 0 where K1 = squrt(2mE) / ħ and K2 = squrt(2m(E- V0)) / ħ (the plus sign in the second one changes into a minus when the particle doesn't have enough energy to overcome the step). Where/How exactly did Schrodinger get these step potential equations from the original one? The step potential equations don't even seem to have the (-ħ2/2m) term in front. Can someone please explain to me why step potentials seem to have different Schrodinger equations than the normal one?