Equations
Advanced formatting examples of real equations from math and physics
Mass-Energy Relation
E
=
m
c
2
where
m
=
Relativistic Mass
c
=
The speed of light in a vacuum
Lorentz Factor Definition
γ
=
1
1
−
v
2
c
2
where
v
=
Velocity
c
=
The speed of light in a vacuum
Relativistic Mass Relation
m
=
γ
m
0
where
m
=
Relativistic Mass
m
0
=
Rest mass
γ
=
Lorentz factor
Observer time
t
′
=
γ
t
−
v
x
x
c
2
where
γ
=
Lorentz factor
t
=
Time
v
x
=
Velocity in the x direction
x
=
x-coordinate
c
=
The speed of light in a vacuum
Observer x
x
′
=
γ
(
x
−
v
x
t
)
where
γ
=
Lorentz factor
t
=
Time
v
x
=
Velocity in the x direction
x
=
x-coordinate
Schrodinger Equation in one dimension
i
ℏ
∂
∂
t
Ψ
(
x
,
t
)
=
−
ℏ
2
2
m
∂
2
∂
x
2
+
V
(
x
,
t
)
Ψ
(
x
,
t
)
where
i
=
Imaginary Unit
t
=
Time
Ψ
=
Schrodinger wave function
ℏ
=
Reduced Planck constant
x
=
x-coordinate
V
=
Potential energy
Correlation Test
χ
2
=
(
x
i
−
x
)
(
y
i
−
y
)
n
i
=
1
(
x
i
−
x
)
2
n
i
=
1
(
y
i
−
y
)
2
n
i
=
1
where
i
=
Summation index
x
=
Independant variable x
y
=
Independant variable y
x
=
Average over all x
y
=
Average over all y
Spherical Electric Field
E
⋅
d
A
=
2
π
R
2
E
where
E
=
Electric Field Vector
A
=
Spherical surface tangent vector
R
=
Sphere radius
E
=
Electric charge
Falling in constant gravity with no air resistance
y
(
t
)
=
y
0
0
v
y0
0
g
d
t
d
t
=
v
y0
t
+
y
0
−
1
2
g
t
2
where
t
=
Time
t
0
=
Initial time
y
=
y-coordinate
v
y0
=
Velocity in the y direction
y
0
=
Initail y position
g
=
Gravitation acceleration at the surface of the earth