Update cheatsheet.en.md

10.temporary-m3p2/16.waves/20.n2/05.waves-introduction/10.waves-in-physics/cheatsheet.en.md

@@ -157,10 +157,10 @@ Since no supporting medium exists for electromagnetic waves, they
    * *X-rays*
    * *gamma rays*
 
-* **Our eyes perceive only** a small part of this spectrum: *visible light*.
+* **Our eyes perceive only** a small part of this spectrum: *visible light*.   
 <br>
 Because **these waves** are **pure energy** (they have no rest mass), they are
-*far more abstract*.
+*far more abstract*.   
 <br>
 At all times, **our bodies are traversed** by *radio waves*, *TV signals*, *WiFi waves* carrying
 music, images, interview speech, etc.
@@ -221,20 +221,30 @@ Our senses cannot perceive these waves at all.
 
 *A - Wave Function and Measurement*
 
-* The **wave function of a particle** (denoted by the Greek letter Psi $`\Psi`$) is governed by the
-  Schrödinger equation in non-relativistic quantum mechanics, or by the Klein-Gordon,
-  Dirac, Proca, Rarita-Schwinger equations (depending on the particle's spin) in quantum
-  field theory (which combines and extends special relativity and quantum mechanics).
+* Quantum waves are **disturbances in a probability field**,
+described by the **wave function $`\psi`$**. The temporal evolution of this function is
+governed by *Schrödinger's equation*, or by more advanced equations in *quantum field theory*
+(which combines and extends special relativity and quantum mechanics).
 
-* It is *not material*, and one of its particularities is to
-  *include an imaginary part* that plays a fundamental role.
+* **$`\boldsymbol{\psi}`$** does not describe a classical wave, but rather a **probability amplitude**
+of finding a particle in a given state (position, momentum, spin, etc.).
+The *probability itself* is proportional to *$`|\boldsymbol{\psi}|^2`*.
+In this sense, the quantum function **$`\boldsymbol{\psi}`$ describes wave-particle duality**.
+
+* It is *not material*, and one of its particularities is
+*having an imaginary component* that plays a fundamental role.
+
+* No one yet fully understands the true meaning of this wave.
+It is **limited by the speed of light, except during measurement**
+(collapse of the wave function), which is a non-local phenomenon, i.e., instantaneous (therefore
+with v > c).
+This **non-local behavior** is *fundamentally random* and thus
+*does not allow communication* (otherwise it would imply the existence of temporal paradoxes).
+
+![](hydrogenoid-atom-quantum-mechanics-s-p-orbitales.gif)
+_Representation of electron presence probability (blue) in s orbitals (center) and p orbitals (8 lobes)_
+_of a hydrogen-like atom, with the atomic nucleus at the center and highly magnified (red)._
 
-* No one yet understands the real meaning of this wave.
-  It is **limited by the speed of light, except at the moment of a measurement**
-  (collapse of the wave function), which is a non-local, i.e., instantaneous phenomenon (therefore
-  with $v > c$).
-  This **non-local behavior** is *fundamentally random* and therefore
-  *does not allow communication* (otherwise, it would imply the existence of temporal paradoxes).
 
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