The task is to find a wavefunction (doesn't need to be normalised) and the energy levels of a particle in an asymmetric potential well (a Schrodinger problem). i.e V = V1 for x<0, 0 for 0<x<d and V = V2 for x>d. What I've got so far is Let α^2= 2m (E-V1)/ℏ^2 β^2= 2mE/ℏ^2 T^2= 2m (E-V2)/ℏ^2 Using these substitutions in Shrodinger's Equations and keeping Ψ finite yields Ψ = A exp (αx) x<0 C exp (iβx) + D exp (-iβx) 0<x<d G exp (-Tx) Boundary conditions give A = C + D Aα = (C - D) iβ Gexp(-Td) = C exp(iβd) + D exp(-iβd) -TGexp(-Td) = Ciβexp(iβd) - Diβexp(-iβd) Eliminating A and G: (C + D) α = (C - D) iβ -T(Cexp(iβd) + Dexp(-iβd)) = iβ(Cexp(iβd) - Dexp(-iβd)) Shifting all these terms of these side onto one side ( so get 0 = .....) and putting into a matrix and setting determinant = 0 yields: (αT - αiβ - Tiβ - β^2)(exp(-iβd)) = (αT + αiβ + Tiβ - β^2)(exp(iβd)) exp(-2iβd) = (αT - αiβ - Tiβ - β^2)/(αT + αiβ + Tiβ - β^2) cos(2βd) -i sin(2βd) = (αT - αiβ - Tiβ - β^2)/(αT + αiβ + Tiβ - β^2) at which point I am stuck. Hints??