Although the overall phase constant of the wave function is of no physical significance...

Although the overall phase constant of the wave function is of no physical significance (it cancels out whenever you calculate a measurable quantity), the relative phase of the coefficients in Equation 2.17 does matter. For example, suppose we change the relative phase of in Problem 2.5:

where is some constant. Find and compare your results with what you got before. Study the special cases (For a graphical exploration of this problem see the apples in footnote 7.)