From Wikipedia, the free encyclopedia
Help:Displaying a formula
x
n
+
1
=
x
n
(
x
n
+
1
)
(
x
n
+
2
)
(
x
n
+
3
)
+
1
{\displaystyle x_{n+1}={\sqrt {x_{n}(x_{n}+1)(x_{n}+2)(x_{n}+3)+1}}}
x_{n+1}=\sqrt{x_n(x_n+1)(x_n+2)(x_n+3)+1}
{\displaystyle }
x^2+y^2
∂
ρ
∂
t
+
∇
⋅
J
=
0
{\displaystyle {\frac {\partial \rho }{\partial t}}+\nabla \cdot \mathbf {J} =0}
.
∂
ρ
∂
t
+
∇
⋅
ρ
v
=
0
{\displaystyle {\frac {\partial \rho }{\partial t}}+\nabla \cdot \rho \mathbf {v} =0}
[
T
(
A
)
∼
T
(
B
)
]
∧
[
T
(
B
)
∼
T
(
C
)
]
⇒
[
T
(
A
)
∼
T
(
C
)
]
{\displaystyle [T(A)\sim T(B)]\wedge [T(B)\sim T(C)]\Rightarrow [T(A)\sim T(C)]}
d
U
=
δ
Q
−
δ
W
{\displaystyle \mathrm {d} U=\delta Q-\delta W\,}
∫
δ
Q
T
≥
0
{\displaystyle \int {\frac {\delta Q}{T}}\geq 0}
T
⇒
0
,
S
⇒
C
{\displaystyle T\Rightarrow 0,S\Rightarrow C}
J
u
=
L
u
u
∇
(
1
/
T
)
−
L
u
r
∇
(
m
/
T
)
{\displaystyle \mathbf {J} _{u}=L_{uu}\,\nabla (1/T)-L_{ur}\,\nabla (m/T)\!}
;
J
r
=
L
r
u
∇
(
1
/
T
)
−
L
r
r
∇
(
m
/
T
)
{\displaystyle \mathbf {J} _{r}=L_{ru}\,\nabla (1/T)-L_{rr}\,\nabla (m/T)\!}
.
∂
f
∂
t
+
∂
f
∂
x
⋅
p
m
+
∂
f
∂
p
⋅
F
=
∫
d
Ω
∫
d
p
1
σ
(
Ω
)
|
p
−
p
1
|
(
f
′
f
1
′
−
f
f
1
)
{\displaystyle {\frac {\partial f}{\partial t}}+{\frac {\partial f}{\partial \mathbf {x} }}\cdot {\frac {\mathbf {p} }{m}}+{\frac {\partial f}{\partial \mathbf {p} }}\cdot \mathbf {F} =\int \mathrm {d} \mathbf {\Omega } \int \mathrm {d} \mathbf {p_{1}} \sigma (\mathbf {\Omega } )|\mathbf {p} -\mathbf {p_{1}} |(f'f'_{1}-ff_{1})}
ρ
(
∂
v
∂
t
+
(
v
⋅
∇
)
v
)
=
ρ
f
−
∇
p
+
μ
(
∇
2
v
+
1
3
∇
(
∇
⋅
v
)
)
{\displaystyle \rho \left({\frac {\partial \mathbf {v} }{\partial t}}+(\mathbf {v} \cdot \nabla )\mathbf {v} \right)=\rho \mathbf {f} -\nabla p+\mu \left(\nabla ^{2}\mathbf {v} +{\frac {1}{3}}\nabla \left(\nabla \cdot \mathbf {v} \right)\right)}
R
μ
ν
−
1
2
g
μ
ν
R
+
g
μ
ν
Λ
=
8
π
G
T
μ
ν
{\displaystyle R_{\mu \nu }-{1 \over 2}g_{\mu \nu }R+g_{\mu \nu }\Lambda ={8\pi }GT_{\mu \nu }}
H
(
t
)
|
ψ
(
t
)
⟩
=
i
ℏ
∂
∂
t
|
ψ
(
t
)
⟩
{\displaystyle H(t)\left|\psi \left(t\right)\right\rangle =\mathrm {i} \hbar {\frac {\partial }{\partial t}}\left|\psi \left(t\right)\right\rangle }
(
α
0
m
c
2
+
∑
j
=
1
3
α
j
p
j
c
)
ψ
(
x
,
t
)
=
i
ℏ
∂
ψ
∂
t
(
x
,
t
)
{\displaystyle \left(\alpha _{0}mc^{2}+\sum _{j=1}^{3}\alpha _{j}p_{j}\,c\right)\psi (\mathbf {x} ,t)=i\hbar {\frac {\partial \psi }{\partial t}}(\mathbf {x} ,t)}
L
Q
C
D
=
q
¯
(
i
γ
μ
∂
μ
−
m
)
q
−
g
(
q
¯
γ
μ
T
a
q
)
G
μ
a
−
1
4
G
μ
ν
a
G
a
μ
ν
{\displaystyle {\mathcal {L}}_{\mathrm {QCD} }={\bar {q}}\left(i\gamma ^{\mu }\partial _{\mu }-m\right)q-g\left({\bar {q}}\gamma ^{\mu }T_{a}q\right)G_{\mu }^{a}-{\frac {1}{4}}G_{\mu \nu }^{a}G_{a}^{\mu \nu }\,}
G
μ
ν
a
=
∂
μ
G
ν
a
−
∂
ν
G
μ
a
−
g
f
a
b
c
G
μ
b
G
ν
c
{\displaystyle G_{\mu \nu }^{a}=\partial _{\mu }G_{\nu }^{a}-\partial _{\nu }G_{\mu }^{a}-gf_{abc}G_{\mu }^{b}G_{\nu }^{c}\,}
4
L
g
=
−
G
a
μ
ν
G
μ
ν
a
−
B
μ
ν
B
μ
ν
{\displaystyle 4{\mathcal {L}}_{\mathrm {g} }=-G_{a}^{\mu \nu }G_{\mu \nu }^{a}-B^{\mu \nu }B_{\mu \nu }}