Question

fal 4 EE 339 Practice Problems 9.1 For a pillbox-shaped cavity with metallic walls, find the lowest energy five cylindrically symmetric wavefunctions. The height of the pill box is 2 nm and its radius is 1 nm. 9.2 The transverse potential energy profile for a circularly symmetric quantum wire embedded in a large radius cladding is approximated for r<ro (ro is the radius of the wire) by a flat potential V%, and for r ro by a zero potential. Compute the energy levels of this electron in this wire, corresponding to cylindrically symmetric wave-functions, if the radius of the wire is 2nm, Vo -0.5 eV, and the effective mass of the electron in both the wire and in the cladding to be the free electron mass. (Let k0). 9.3 Find the lowest five eigenvalues corresponding to spherically symmetric states of an electron entrapped in a metalized surface sphere of radius R, where R 3 nm.

Answer 1

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