Question

4. (20 points) Infinite Wells in Three Dimensions a) Consider a three dimensional in- finite rectangular well for which L -L, Ly-2L, ald L2-3L. In terms of quantum numbers (e.g. nz, ny, and n.), M. L, and ћ. write down an expression for the energies of all quantum states. (b) Find the energies of the ground state and the first three lowest lying energies. As in part (b), for each energy level, give the quantum numbers n, ny, n and indicate the degeneracy. Note: there is no need in this case to sketch the nodal configurations of the quantum states (c) Consider a quantum dot consisting of a cubic infinite square well where the length of each edge is L. The well confines electrons, for which M 9.109 x 10-31 kg. A colloidal suspension of such quantum dots appears bluish due to 450 nanometer pho- tons emitted as the second excited state decays to the ground state. Based on this information, calculate the size L of the quantum dots in nanometers. Note that one has a first excited state above the ground state and then the second excited state under consideration. An added consideration is the fact that, as is true for the first excited state, there may be a degeneracy in the second excited state. Nevertheless, whether the state is degenerate or not, the analysis to find L will stl be feasible

Answer 1

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