In class we chose our 1-D box to go from x = 0 to x = L. Suppose we instead chose our box to go from x = -L to x = L.
a) Use the boundary conditions to show Psi_n(x) = ( 1/L )^(1/2) sin (n*pi*x/2L), n=even; Psi_n(x) = ( 1/L )^(1/2) cos (n*pi*x/2L), n=odd. Hint: As a visual aid draw the first two wave functions for n = 1 and n = 2.
b) Determine the energy levels. Are they the same as the ones for a box going from x = 0 to x = 2L?
c) Show that ?x?p ≥ ?/2 for this - L to L box.