Proving the Relation in "Methods of Theoretical Physics

[arbri]

Homework Statement

In "Methods of theoretical physics" from the authors Morse and Feshbach is writen:
" The displacement (dx,dy,dz) is perpendicular to the surface if the component displacemetn satisfy the equation:

[Broken]

How to prove this relation?

Homework Equations

the relevant equation is the equation of total change

The Attempt at a Solution

 

[tiny-tim]

hi arbri! welcome to pf!

In "Methods of theoretical physics" from the authors Morse and Feshbach is writen:
" The displacement (dx,dy,dz) is perpendicular to the surface if the component displacemetn satisfy the equation:

$$\frac{dx}{\partial \psi /\partial x} = \frac{dy}{\partial \psi /\partial y} = \frac{dz}{\partial \psi /\partial z}$$

How to prove this relation?

that's just (dx,dy,dx)·∇ψ = 0