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. Consider a potential

where V(x)= co for x < 0 and V(x) = kx? for x > 0. Write the two lowest b) energy wavefunctions for this potential. How do these compare to the wavefunctions for the simpleharmonic oscillator? c) Describe what is meant for the SH0 wavefunction to tunnel. d) Do these wave functions tunnel into the potential and if so, how much compared to the analogous SHO