For the same system as in Exercise E7C.4(a) (Functions of the form cos(nπx/L), where n = 1, 3, 5 …, can be used to model the wavefunctions of particles confined to the region between x = −L/2 and x = +L/2. The integration is limited to the range −L/2 to +L/2 because the wavefunction is zero outside this range. Show that the wavefunctions are orthogonal for n = 1 and 3. You will find the necessary integral in the Resource section), show that the wavefunctions with n = 3 and 5 are orthogonal.

For the same system as in Exercise E7C.4(a) (Functions of the form cos(nπx/L), where n = 1, 3, 5 …, can be used to model the wavefunctions of particles confined to the region between x = −L/2 and x = +L/2. The integration is limited to the range −L/2 to +L/2 because the wavefunction is zero outside this range. Show that the wavefunctions are orthogonal for n = 1 and 3. You will find the necessary integral in the Resource section), show that the wavefunctions with n = 3 and 5 are orthogonal.