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E 1. E 2. E 3. Graphically solve for E n ’s, now know α n ’s and k n ’s. E 1 =0.0675eV k 1 =1.366E9 α 1 =4.9656E9 E 2 =0.291eV k 2 =2.7789E9 α 2 =4.3298E9 E 3 =0.714eV k 3 =4.345E9 α 3 =2.75E9. Psi1, not normalized. Psi1, normalized. Psi2, Normalized.
E N D
E1 E2 E3
Graphically solve for En’s, now know αn’s and kn’s • E1=0.0675eV • k1=1.366E9 • α1=4.9656E9 • E2=0.291eV • k2=2.7789E9 • α2=4.3298E9 • E3=0.714eV • k3=4.345E9 • α3=2.75E9
To find area outside of well, simply integrate Psi*Psidx outside of well • For Psi1: Probability outside of well is 1.13% • For Psi2: Probability outside of well is 3.79%
To find <x> and <p> use the operator expression and integrate • For Psi1, <x1> = 0.979nm …should be 1nm • For Psi2, <x2> = .917nm, …should be 1nm • For Psi1, <p1> = i*3.13E-27 • For Psi2, <p2> = i*1.38E-26
Problem 2 • Use notes from lecture to determine E1,E2,E3 and Psi1, Psi2, Psi3.
Perform Integration to find Mmn • M21= 0.36nm • M31=1.4x10-8nm ~ 0 • M32=0.39nm