Quantum Dot Energy Harvester · AI Generator #GEN-877815E8

Physics · quantum-mechanics

Problem

A novel energy harvesting device consists of a quantum dot (modeled as a 3D infinite square well) that can absorb photons and emit electrons. The quantum dot is a cube with side length L=2.0×10−9  mL = 2.0 \times 10^{-9}\;\text{m}. When the device operates, electrons in the ground state absorb photons of wavelength λ=800  nm\lambda = 800\;\text{nm} and are promoted to the first excited state. However, due to quantum confinement effects, the actual potential well has slightly "soft" walls that can be modeled as a small perturbation. The perturbing potential is: V′(x,y,z)=V0(sin⁡2(πxL)+sin⁡2(πyL)+sin⁡2(πzL))V'(x,y,z) = V_0 \left(\sin^2\left(\frac{\pi x}{L}\right) + \sin^2\left(\frac{\pi y}{L}\right) + \sin^2\left(\frac{\pi z}{L}\right)\right) where V0=0.050  eVV_0 = 0.050\;\text{eV}. (a) Calculate the ground state energy of the unperturbed 3D infinite square well. (b) Using first-order perturbation theory, find the shift in the ground state energy due to the soft walls. (c) Determine whether the 800  nm800\;\text{nm} photons can still promote electrons from the perturbed ground state to the first excited state (assume the first excited state energy is not significantly affected by the perturbation).

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