Consider a single electron confined to a one-dimensional quantum well device of length L = 0.5 nm. The quantum well device acts as a “trap” for the electron 1.What are the boundary conditions for this system? Apply them to show that ψn(x) = Asin(nπx/L), n = 1,2,3,... (check image) 2.Normalize the wave function to find the constant A. 3. Sketch ψ1, ψ2, and ψ3, as well as |ψ1|2, |ψ2|2, and |ψ3|2, and evaluate the energy levels E1, E2, and E3 in eV. 4. Suppose the particle is in the first excited state. What is the probability of finding the particle between x = L/4 and x = 3L/4? 5. Suppose, instead of one electron, we trap five electrons in the quantum well. Draw an energy-level diagram to show the electron configuration of the ground state. What is the ground state energy?
Consider a single electron confined to a one-dimensional quantum well device of length L = 0.5 nm. The quantum well device acts as a “trap” for the electron
1.What are the boundary conditions for this system? Apply them to show that ψn(x) = Asin(nπx/L), n = 1,2,3,...
(check image)
2.Normalize the wave function to find the constant A.
3. Sketch ψ1, ψ2, and ψ3, as well as |ψ1|2, |ψ2|2, and |ψ3|2, and evaluate the energy levels E1, E2, and E3 in eV.
4. Suppose the particle is in the first excited state. What is the probability of finding the particle between x = L/4 and x = 3L/4?
5. Suppose, instead of one electron, we trap five electrons in the quantum well. Draw an energy-level diagram to show the electron configuration of the ground state. What is the ground state energy?
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