Update vol-III-chap-9-sect-2.md

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 ## 9.2. Correspondence and uncertainty principles in Quantum Physics.
 
-The mathematical treatment of the concept of matter wave proposed by de Broglie requires that the motion of a quantum particle at a point $\vec{r}$ and at time $t$ must be described by a function of wave nature, the so-called wave function, which is represented as $ψ(\vec{r},t)$. This wave function has no physical meaning. It is the square of its absolute value, the probability density $P = │ψ(\vec{r],t)│^2$, that determines experimentally when and where the particle described by the wave function $ψ(\vec{r},t)$ is at position $\vec{r}(t)$ at time $t$.
+The mathematical treatment of the concept of matter wave proposed by de Broglie requires that the motion of a quantum particle at a point $\vec{r}$ and at time $t$ must be described by a function of wave nature, the so-called wave function, which is represented as $ψ(\vec{r},t)$. This wave function has no physical meaning. It is the square of its absolute value, the probability density $P = │ψ(\vec{r},t)│^2$, that determines experimentally when and where the particle described by the wave function $ψ(\vec{r},t)$ is at position $\vec{r}(t)$ at time $t$.
 
 According to Newtonian mechanics, the equation of motion for classical particles of mass $m$ and velocity $\vec{v}$ is $\vec{F} = d\vec{p}/dt$, where $\vec{p} = m\vec{v}$ is its linear momentum. Will this classical mechanics be appropriate to describe the movement of matter waves proposed by de Broglie? Let us see and suppose that $\vec{u}$ is the velocity with which such a wave propagates; this will corresponds to the velocity $v$ with which the particle described by the wave function $ψ(\vec{r},t)$ moves. If this movement is in the direction of the X-axis, the wave function will be $ψ(x,t)$.