(a) Write down (no derivation needed) the time-independent Schrödinger equation for the region inside the well, giving an explicit expression for H. (b) Write down (no derivation needed) an explicit general expression for i) the spatial parts of the energy eigenfunctions, and ii) the energy eigenvalues for the particle in this system. Determine the two lowest energy levels that are degenerate (degeneracy> 1-fold) and determine their degeneracy. Show your reasoning.
(a) Write down (no derivation needed) the time-independent Schrödinger equation for the region inside the well, giving an explicit expression for H. (b) Write down (no derivation needed) an explicit general expression for i) the spatial parts of the energy eigenfunctions, and ii) the energy eigenvalues for the particle in this system. Determine the two lowest energy levels that are degenerate (degeneracy> 1-fold) and determine their degeneracy. Show your reasoning.
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Transcribed Image Text:3. Consider a quantum particle in a three-dimensional infinite well with edge lengths of a
along and y and 2a along z, e.g. walls at x = 0, x= a, y = 0, y = a, z = 0 and z = 2a.
(a) Write down (no derivation needed) the time-independent Schrödinger equation for the
region inside the well, giving an explicit expression for H.
(b) Write down (no derivation needed) an explicit general expression for
i) the spatial parts of the energy eigenfunctions, and
ii) the energy eigenvalues for the particle in this system.
Determine the two lowest energy levels that are degenerate (degeneracy> 1-fold) and
determine their degeneracy. Show your reasoning.
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