The half harmonic potential a) Give a physical reason for why wavefunctions of symmetric potentials (V(x) = V(-x))) should be either even (symmetric) or odd (antisymmetric) functions. b) Consider a potential where V(x) = 0 for x 0. Write the two lowest energy wavefunctions for this potential. How do these compare to the wavefunctions for the simple harmonic oscillator? c) Explain what is meant for the SHO wavefunction to tunnel. d) Do particles in the half-harmonic potential tunnel into the potential and if so, how much compared to the analogous SHO wavefunctions