Using the one-dimensional (1-D) Schr¨odinger equation, derive the expressions of quantized energy states for (i) an infinite square well (with well width a = 100 A), (ii) triangular well, and (iii) parabolic well. Assuming ˚ that the quantization occurs in the z-direction and the potential energies for the three cases are given by (i) U(z) → ∞ (ii) U(z) = qEz (where E is the electric field inside the triangular well), and (iii) U(z) = m∗(ω2/2)z2, calculate the energy levels of the ground state and the first excited state of (i) and (ii). Given: m∗ = 0.067m0, a = 100 A, and ˚ E = 105 V/cm
