1. The problem statement, all variables and given/known data Consider the semi-infinite square well given by V(x) = -V0 < 0 for 0≤ x ≤ a and V(x) = 0 for x > a. There is an infinite barrier at x = 0 (hence the name "semi-infinite"). A particle with mass m is in a bound state in this potential with energy E ≤ 0. Solve the Schrodinger equation to derive ψ(x) for x ≥ 0. Use the appropriate boundary conditions and normalize the wave function so that the final answer does not contain any arbitrary constants. 2. Relevant equations [-h_bar2/2m]ψ'' + V(x)ψ = Eψ 3. The attempt at a solution Schrodinger Equation for 0 ≤ x ≤ a and x > a: [-h_bar2/2m]ψ'' - V0ψ = Eψ, 0 ≤ x ≤ a [-h_bar2/2m]ψ'' = Eψ, x ≥ a Rewrite Schrodinger equations: ψ'' + 2m(E+V0)/h_bar2 = 0, 0 ≤ x ≤ a ψ'' + 2mE/h_bar2 = 0, x ≥ a Solve Schrodinger equations: ψ1 = A1eik1x + B1e-ik1x, k1 = sqrt[2m(E+V0)]/h_bar, 0 ≤ x ≤ a ψ2 = A2eik2x + B2e-ik2x, k2 = sqrt[2mE]/h_bar, x ≥ a k2 is negative, and the wave function must not blow up at x = ∞, so A2 = 0: ψ1 = A1eik1x + B1e-ik1x, k1 = sqrt[2m(E+V0)]/h_bar, 0 ≤ x ≤ a ψ2 = B2e-ik2x, k2 = sqrt[2mE]/h_bar, x ≥ a Apply boundary conditions: ψ1(0) = 0 ψ1(a) = ψ2(a) ψ'1(a) = ψ'2(a) 1st condition: A1 + B1 = 0 2nd condition: A1eik1a + B1e-ik1a = B2e-ik2a 3rd condition: ik1A1eik1a - ik1B1e-ik1a = -ik2B2e-ik2a Now I have 3 equations for 3 unknowns, A1, B1, and B2. But I have been trying to solve this algebraically for quite awhile, and I just can't get it to work. When I solve A1 and B1 in terms of B2 and try to plug them into the third condition, I just get B2 cancelling on both sides. Maybe I'm being really dumb about basic math but I would really appreciate if someone could help with this. Thanks!