Problem 2.6 – Griffith’s Intro to QM

Problem 2.6

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 $\psi_1$ and $\psi_2$ in Problem 2.5:

$\Psi (x,0) = A[\psi_1 (x) + e^{i \phi}\psi_2 (x)],$

where $\phi$ is some constant. Find $\Psi (x,t)$ , $|\Psi (x,t)|^2$ , and $\langle x \rangle$ , and compare your results with what you got before. Study the special cases $\phi = \pi/2$ and $\phi = \pi$ . (For a graphical exploration of this problem see the applet in footnote 9 of this chapter.)