By Levi A.F.J.
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Additional resources for Applied quantum mechanics: Solutions manual
50 × m 0 . (d) Plot the Fermi-Dirac distribution function for the situations described by (b) and (c). (e) Repeat (b), (c), and (d), only now for the case when temperature T = 77 K . Your answer should include a print out of your computer program and plots. PROBLEM 2 1 1 (a) Show that ------------------------------= 1 – -----------------------------( E – µ) ⁄ k B T (µ – E ) ⁄ kB T e +1 e +1 (b) A semiconductor consists of a valance band with electron energy dispersion relation EVB = E ( k ) and a conduction band with electron energy dispersion relation such that EC B = E 0 – E ( k ) , where E0 is a constant such that the conduction band and valence band are separated by an energy band gap, E g .
Comment on your result. PROBLEM 3 An electron is initially in the ground state of a one-dimensional rectangular potential well for which V ( x ) = 0 in the range 0 < x < L and V ( x ) = ∞ elsewhere. The ground state energy is E1 and the first excited state energy is E 2 . At time t = 0 the sys2 –t ⁄ τ tem is subject to a perturbation V ( x , t ) = V0 x e . Calculate and then use a computer program to plot the probability of finding the particle in the first excited state as a function of time for t ≥ 0 .
PROBLEM 2 An electron is in ground state of a one-dimensional rectangular potential well for which V ( x ) = 0 in the range 0 < x < L and V ( x ) = ∞ elsewhere. It is decided to control the state of the electron by applying a pulse of electric field E ( t ) = E 0 e 2 –t ⁄ τ 2 ⋅ xˆ at time t = 0, where τ is a constant, xˆ is the unit vector in the x-direction, and E 0 is the maximum strength of the applied electric-field. (a) Calculate the probability P 12 that the particle will be found in the first excited state in the long time limit, t → ∞ .
Applied quantum mechanics: Solutions manual by Levi A.F.J.