Misner,Thorne, Wheeler - Exercise 2.1 : 1-form as the de Broglie wave's surface

Question

Can anyone offer a solution (or hint) to exercise 2.1 of Misner,Thorne, Wheeler - "Gravitation", stating:

"Show that equation $\textbf{p}\cdot \textbf{v}=\langle\tilde{\textbf{p}},\textbf{v}\rangle$ is in accord with the quantum-mechanical properties of a de Broglie wave, $\psi = e^{i\phi}=\exp[i(\textbf{k}\cdot \textbf{x}-\omega t)]$"

$\textbf{p}$ stands for the momentum vector 

$\tilde{\textbf{p}}$ stands for "momentum 1-form"

$\textbf{v}$ is any vector 

Thank you for your help.

Comments

Voting to close as low-level.