For (i) the infinite square well, (ii) the finite square well and (iii) the quantum harmonic oscillator, carefully sketch each of the following: a) The potential and the energy levels of the two lowest energy eigenstates. b) The wavefunctions for the two lowest energy eigenstates. c) The probability densities for the two lowest energy eigenstates. In the case of the finite square well, assume that the well admits exactly two energy eigenstates.

For (i) the infinite square well, (ii) the finite square well and (iii) the quantum harmonic oscillator, carefully sketch each of the following: a) The potential and the energy levels of the two lowest energy eigenstates. b) The wavefunctions for the two lowest energy eigenstates. c) The probability densities for the two lowest energy eigenstates. In the case of the finite square well, assume that the well admits exactly two energy eigenstates.