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 and in Problem 2.5:

Equation 2.17

where ϕ is some constant. Find Ψ (x,t) and |Ψ (x,t)|², and , and compare your results with what you got before. Study the special cases ϕ = π/2 and ϕ = π. (For a graphical exploration of this problem see the applet in footnote 9 of this chapter.)

(x, 0) = A [v (x) + c2 (x)],