6. (10 points) Consider the three-dimensional extension of the infinite well potential, in which a particle is confined to an L x L x L region of space. By following a procedure essentially identical to the one for the two-dimensional case described at the end of section 5.4 in our textbook, we could derive the expression for the energy levels of this quantum system. This turns out to be E = ħ²² 2mL2 == (n²+n+n²) = Eo (n²+n²+n²) where n, ny, and n₂ are integers > 1. Sketch an energy level diagram (similar to Figure 5.16 in our book) for the first 10 distinct energy levels of this system. Be sure to indicate the energy (in terms of Eo, for brevity), quantum numbers, and degeneracy of each energy level. 7. (10 points) The wavefunction (x)=Cxe-ax² describes the first excited state of the quantum harmonic oscillator. (a) Following along with the method described in section 5.5 of our textbook, find an expression for the constant a for this wavefunction in terms of the particle mass m and the classical oscillation frequency wo (b) Find the energy E of this state. (c) Find the normalization constant C. You will want to have an integral table handy.