$$c=\lambda \nu\\
Q_f=Q_i(\frac{1}{2})^{\frac{T_f}{T_0.5}}\\
E=h\frac{c}{\lambda}=h\nu\\
\Delta x \cdot \Delta v > \frac{h}{4\pi m}\\
e,E_i,A=\frac{n}{r}\\
$$
Werner
$$sen α sen β = \frac{1}{2}[cos(α - β) - cos(α + β)]\\
cos α cos β = \frac{1}{2}[cos(α - β) + cos(α + β)]\\
sen α cos β = \frac{1}{2}[sen(α - β) + sen(α + β)]$$
Geometria analitica
Retta
$$y=mx+q \lor ax+by+c=0\\
m=\frac{y_A-y_B}{x_A-x_B}\\
y-y_0=m(x-x_0)\\
r \perp s \Rightarrow m=-\frac{1}{m'}\\
r \parallel s \Rightarrow m=m'\\
d =\frac{|ax_0+by_0+c|}{\sqrt{a^2+b^2}} \\
P \in r \Rightarrow f(x_p,y_p) = 0$$
Fascio
$$ax +by +c +k(a'x+b'x+c)=0\\
\frac{a}{b} \neq \frac{a'}{b'} \Rightarrow \exists C\\
\frac{a}{b} = \frac{a'}{b'} \Rightarrow \nexists C$$
Parabola
$$a \parallel (x=0) \Rightarrow y = ax^2+bx+c\\
V(-\frac{b}{2a};-\frac{\Delta}{4a}) \land F(-\frac{b}{2a};\frac{1-\Delta}{4a})\\
a:x=-\frac{b}{2a} \land d:y=-\frac{1+\Delta}{2a}\\
a \parallel (y=0) \Rightarrow x = ay^2+by+c\\
V(-\frac{\Delta}{4a};-\frac{b}{2a}) \land F(\frac{1-\Delta}{4a};-\frac{b}{2a})\\
a:y=-\frac{b}{2a} \land d:x=-\frac{1+\Delta}{2a}$$
Fascio
$$y-ax^2-bx-c+k(y-a'x^2-b'x-c) = 0$$
Circonferenza
$$x^2+y^2+ax+by+c=0\\
C(-\frac{a}{2};-\frac{b}{2}) \land r = \sqrt{x_C^2+y_C^2-c}$$
Fascio
$$x^2+y^2+ax+by+c+k(x^2+y^2+a'x+b'y+c')=0$$
Formula sdoppiamento
$$x^2=xx_0 \land y^2=yy_0\\
x=\frac{x+x_0}{2} \land y=\frac{y+y_0}{2}$$
Condizioni per coefficienti
Retta
in formula $$r: ax+by+c=0$$
$$a=0 \Rightarrow r: y=-\frac{c}{b}\\
b=0 \Rightarrow r: x=-\frac{c}{a}\\
c=0 \Rightarrow O \in r$$
Parabola
in formula $$\gamma: y=ax^2+bx+c=0$$
$$b=0 \Rightarrow V(0;c)\\
c=0 \Rightarrow O \in \gamma\\
b=c=0 \Rightarrow V \equiv O$$
Circonferenza
in formula $$\gamma: x^2+y^2+ax+by+c=0$$
$$a=0 \Rightarrow C(0;y_C)\\
b=0 \Rightarrow C(x_C;0)\\
c=0 \Rightarrow O \in \gamma\\
a=b=0 \Rightarrow C \equiv O \land r=\sqrt{-c}\\
a=c=0 \Rightarrow C(0;y_C) \land O \in \gamma\\
b=c=0 \Rightarrow C(x_C;0) \land O \in \gamma$$
