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## Energy Drift - If n = -1, E1 = h2 / 8ma2, ψ1 = √(2/a)sin(π/a)x - If n = 2, E2 = 4h2 / 8ma2, ψ2 = √(2/a)sin(2π/a)x - If n = 3, E3 = 9h2 / 8ma2, ψ3 = √(2/a)sin(3π/a)x ### Energy Difference ΔE - ΔE = E2 - E1 = 4h2/8ma2 = 3h2/8ma2 - ΔE = E3 - E2 = 9h2/8ma2 - 4h2/8ma2 = 5h2/8ma2 ## HOMO and LOMO -...

## Energy Drift - If n = -1, E1 = h2 / 8ma2, ψ1 = √(2/a)sin(π/a)x - If n = 2, E2 = 4h2 / 8ma2, ψ2 = √(2/a)sin(2π/a)x - If n = 3, E3 = 9h2 / 8ma2, ψ3 = √(2/a)sin(3π/a)x ### Energy Difference ΔE - ΔE = E2 - E1 = 4h2/8ma2 = 3h2/8ma2 - ΔE = E3 - E2 = 9h2/8ma2 - 4h2/8ma2 = 5h2/8ma2 ## HOMO and LOMO - n = 1/2 --> HOMO - n = 3/2 --> LOMO ## Finding the HOMO and LOMO Energy Gap for the Energy Level System - E = (n + 1)2h2 / 8π2a2m, ψ = √(2/a)sin((n+1)π/a)x - If n = 1, E1 = 4π2h2/8π2a2m, ψ1 = √(2/a)sin(2π/a)x - E1 = h2/2a2m