: The quantum mechanical simple harmonic oscillator a) Use the recursion relationship to write the wave functions for the 6 lowest energy wave functions of the SHO. b) Explain why

the shapes of the first 3 lowest energy wave functions of the SHO make physical sense. c) Explain why the higher energy states of the SHO spend more time near the classical turning points. d) Show that the ground state and first excited state are eigenfunctions of the Hamiltonian.