symbol ID  category  latex  scope  dimensionality  name  value  Used in derivations  references  use count 

2321  variable 
\omega
\(\omega\) 
['real'] 

angular frequency  21  
2941  variable 
n_1
\(n_1\) 
['real'] 

index of refraction for material 1  9  
4929  variable 
KE
\(KE\) 
['real'] 

kinetic energy  7  
4930  variable 
PE
\(PE\) 
['real'] 

potential energy  4  
4931  variable 
E
\(E\) 
['real'] 

energy  10  
1134  variable 
p
\(p\) 
['real'] 

momentum  15  
4928  variable 
\theta_{\rm Brewster}
\(\theta_{\rm Brewster}\) 
['real'] 

Brewster's angle  16  
1157  constant 
k_{Boltzmann}
\(k_{Boltzmann}\) 
['real'] 

Boltzmann constant 
1.38064852 10^{23} meter^2 kilogram second^2 Kelvin^1 
1  
1054  constant 
\hbar
\(\hbar\) 
['real'] 

Reduced Planck's constant 
1.0545718*10^{34} meter^2 kilogram second^1 
33  
1357  variable 
v
\(v\) 
['real'] 

velocity 

80  
1370  constant 
\alpha
\(\alpha\) 
['real'] 

finestructure constant 
1/137.03599999 dimensionless 
5  
1452  variable 
y
\(y\) 
['real'] 

13  
1464  variable 
x
\(x\) 
['real'] 


140  
1467  variable 
t
\(t\) 
['real'] 

time 

120  
1469  variable 
y_0
\(y_0\) 
['real'] 

initial position  9  
1552  variable 
j
\(j\) 
['integer'] 

index  7  
1567  variable 
i
\(i\) 
['integer'] 

index  1  
1572  variable 
x_0
\(x_0\) 
['real'] 

initial position  11  
1900  variable 
d
\(d\) 
['real'] 

0  
2718  constant 
\exp
\(\exp\) 
['real'] 

e 
2.71828 unitless 
8  
1999  constant 
e
\(e\) 
['real'] 

charge of an electron 
1.602*10^{19} Columb 
6  
2467  variable 
t_f
\(t_f\) 
['real'] 

final time  15  
2911  variable 
\vec{x}
\(\vec{x}\) 
['vector'] 

position  0  
3141  constant 
\pi
\(\pi\) 
['real'] 

pi 
3.1415 dimensionless 
55  
4202  variable 
F
\(F\) 
['real'] 

force  21  
4201  variable 
f
\(f\) 
['real'] 

frequency  8  
4200  variable 
f
\(f\) 
['real'] 

0  
4221  variable 
u
\(u\) 
['real'] 

5  
4231  variable 
c
\(c\) 
['real'] 

12  
4291  variable 
g
\(g\) 
['real'] 

0  
4567  constant 
c
\(c\) 
['real'] 

speed of light in vacuum 
299792458 meters/second 
32  
4568  variable 
t_0
\(t_0\) 
['real'] 

time 0  0  
4621  variable 
i
\(i\) 
['imaginary'] 

imaginary unit 

74  
5156  variable 
m
\(m\) 
['real'] 

mass 

57  
5321  variable 
k
\(k\) 
['real'] 

angular wavenumber  13  
5563  variable 
t_i
\(t_i\) 
['real'] 

initial time  0  
6022  constant 
N_A
\(N_A\) 
['real'] 

Avagadro's constant 
6.02214086*10^{23} mol^1 
0  
9140  variable 
a
\(a\) 
['real'] 

acceleration  31  
9139  variable 
a
\(a\) 
['real'] 

45  
1939  variable 
b
\(b\) 
['real'] 

20  
9199  variable 
dx
\(dx\) 
['real'] 

15  
9491  variable 
T
\(T\) 
['real'] 

period  8  
1115  variable 
\lambda
\(\lambda\) 
['real'] 

wavelength  5  
1943  variable 
d
\(d\) 
['real'] 

displacement  25  
3034  variable 
C
\(C\) 
['real'] 

circumference  5  
2530  variable 
r
\(r\) 
['real'] 

radius  34  
6081  constant 
r_{\rm Earth\ orbit}
\(r_{\rm Earth\ orbit}\) 
['real'] 

radius of Earth's orbit 
1.496*10^8 km 
5  
4037  variable 
x
\(x\) 
['real'] 

position 

52  
5456  variable 
x'
\(x'\) 
['real'] 

position in moving reference frame  3  
1888  variable 
y'
\(y'\) 
['real'] 

position in moving reference frame  2  
4306  variable 
z'
\(z'\) 
['real'] 

position in moving reference frame  2  
6728  variable 
z
\(z\) 
['real'] 

position  5  
5647  variable 
y
\(y\) 
['real'] 

position  13  
1790  variable 
\gamma
\(\gamma\) 
['real'] 

Lorentz factor  35  
5153  variable 
v_0
\(v_0\) 
['real'] 

initial velocity  44  
4453  variable 
A
\(A\) 
['complex'] 

none  23  
4698  variable 
B
\(B\) 
['complex'] 

none  19  
3192  variable 
Z
\(Z\) 
['complex'] 

none  9  
1575  variable 
\theta
\(\theta\) 
['real'] 

angle  34  
8586  variable 
\phi
\(\phi\) 
['real'] 

angle  10  
7882  variable 
I
\(I\) 
['real'] 

intensity  9  
8251  variable 
I_{\rm coherent}
\(I_{\rm coherent}\) 
['real'] 

intensity of coherent waves  4  
2435  variable 
I_{\rm incoherent}
\(I_{\rm incoherent}\) 
['real'] 

intensity of incoherent waves  4  
1649  variable 
g
\(g\) 
['real'] 

acceleration due to gravity  27  
2958  variable 
v_{0, x}
\(v_{0, x}\) 
['real'] 

initial velocity along x axis  15  
9431  variable 
v_{0, y}
\(v_{0, y}\) 
['real'] 

initial velocity along y axis  12  
6091  variable 
\vec{v}_0
\(\vec{v}_0\) 
['real'] 

initial velocity  1  
4711  variable 
dt
\(dt\) 
['real'] 

differential time 

7  
5674  variable 
d v_y
\(d v_y\) 
['real'] 

differential velocity along y axis  2  
5005  variable 
d v_x
\(d v_x\) 
['real'] 

differential velocity along x axis  2  
5842  variable 
dy
\(dy\) 
['real'] 

differential displacement along y axis 

2  
7092  variable 
y_f
\(y_f\) 
['real'] 

final position on y axis  4  
3652  variable 
x_f
\(x_f\) 
real 

final position on x axis  4  
1592  variable 
n
\(n\) 
integer 

index  23  
2523  variable 
W
\(W\) 
real 

width  25  
6789  variable 
W
\(W\) 
real 

work  10  
1088  variable 
W
\(W\) 
real 

work done to a system  1  
9398  variable 
dW
\(dW\) 
real 

differential work 

2  
5458  constant 
m_{\rm Earth}
\(m_{\rm Earth}\) 
real 

mass of Earth 
5.97237*10^24 kg 
34  
6277  constant 
G
\(G\) 
real 

gravitational constant 
6.67430*10^{11} m^3 * kg^1 * s^2 
46  
3236  constant 
r_{\rm Earth}
\(r_{\rm Earth}\) 
real 

radius of Earth 
6.3781*10^{6} m 
21  
8656  variable 
v_{\rm escape}
\(v_{\rm escape}\) 
real 

escape velocity  12  
4518  variable 
r_{\rm Schwarzschild}
\(r_{\rm Schwarzschild}\) 
real 

Schwarzschild radius; event horizon  5  
6599  variable 
V
\(V\) 
real 

voltage  11  
8257  variable 
V_1
\(V_1\) 
real 

voltage  3  
8721  variable 
V_2
\(V_2\) 
real 

voltage  3  
4501  variable 
I
\(I\) 
real 

electric current  9  
3978  variable 
I_1
\(I_1\) 
real 

electric current  4  
4856  variable 
I_2
\(I_2\) 
real 

electric current  4  
6458  variable 
R
\(R\) 
real 

electrical resistance  6  
8697  variable 
R_1
\(R_1\) 
real 

electrical resistance  10  
3461  variable 
R_2
\(R_2\) 
real 

electrical resistance  10  
1908  variable 
R_{\rm total}
\(R_{\rm total}\) 
real 

electrical resistance  9  
9647  variable 
I_{\rm total}
\(I_{\rm total}\) 
real 

electric current  4  
4691  variable 
V_{\rm total}
\(V_{\rm total}\) 
real 

voltage  2  
7557  constant 
g_{\rm Earth}
\(g_{\rm Earth}\) 
real 

average acceleration due to gravity on Earth 
9.80665 m * s^2 
6  
5177  variable 
v
\(v\) 
real 

none 

2  
4989  variable 
t'
\(t'\) 
real 

time in moving reference frame 

7  
8339  variable 
\hat{x}
\(\hat{x}\) 
real 

unit vector  4  
1700  variable 
\hat{y}
\(\hat{y}\) 
real 

unit vector  4  
5598  variable 
\hat{A}
\(\hat{A}\) 
real 

observerable operator  3  
3410  variable 
h
\(h\) 
real 

none 

2  
1955  variable 
KE_1
\(KE_1\) 
real 

kinetic energy  17  
1352  variable 
KE_2
\(KE_2\) 
real 

kinetic energy  14  
4093  variable 
PE_1
\(PE_1\) 
real 

kinetic energy  12  
8849  variable 
PE_2
\(PE_2\) 
real 

potential energy  11  
3509  variable 
\theta_1
\(\theta_1\) 
real 

angle  2  
7545  variable 
\theta_2
\(\theta_2\) 
real 

angle  2  
1958  variable 
n_2
\(n_2\) 
real 

index of refraction for material 2  8  
5022  variable 
m_1
\(m_1\) 
real 

mass  18  
4851  variable 
m_2
\(m_2\) 
real 

mass  17  
3569  variable 
m_{\rm satellite}
\(m_{\rm satellite}\) 
real 

mass of satellite  6  
4082  variable 
v_{\rm satellite}
\(v_{\rm satellite}\) 
real 

velocity of satellite  4  
4413  variable 
h
\(h\) 
real 

Planck's constant  5  
2243  variable 
\theta_{\rm refracted}
\(\theta_{\rm refracted}\) 
real 

refracted angle 

2  
3852  variable 
x_1
\(x_1\) 
real 

position 1 

5  
5467  variable 
x_2
\(x_2\) 
real 

position 2 

5  
5579  variable 
E_1
\(E_1\) 
real 

energy 1 

9  
4550  variable 
E_2
\(E_2\) 
real 

energy 2 

9  
2473  variable 
v_1
\(v_1\) 
real 

velocity 1  14  
4770  variable 
v_2
\(v_2\) 
real 

velocity 2  14  
6709  variable 
v_{\rm average}
\(v_{\rm average}\) 
real 

velocity average  2  
8762  variable 
T_{\rm orbit}
\(T_{\rm orbit}\) 
real 

orbital period  9  
5595  variable 
T_{\rm geostationary\ orbit}
\(T_{\rm geostationary\ orbit}\) 
real 

geostationary orbital period  3  
1534  variable 
C_{\rm Earth\ orbit}
\(C_{\rm Earth\ orbit}\) 
real 

circumference of Earth's orbit  4  
1687  variable 
F_{\rm centripetal}
\(F_{\rm centripetal}\) 
real 

centripetal force  3  
2867  variable 
F_{\rm gravity}
\(F_{\rm gravity}\) 
real 

force due to gravity  3  
9107  variable 
v_y
\(v_y\) 
real 

velocity along y axis 

7  
6722  variable 
du
\(du\) 
real 

differential of u 

0  
6694  variable 
dv
\(dv\) 
real 

differential of v 

0  
5332  variable 
KE_{\rm escape}
\(KE_{\rm escape}\) 
real 

kinetic energy of escape velocity 

4  
6431  variable 
PE_{\rm Earth\ surface}
\(PE_{\rm Earth\ surface}\) 
real 

potential energy at the Earth's surface 

4  
7159  variable 
a_x
\(a_x\) 
real 

acceleration along x axis  4  
7055  variable 
a_y
\(a_y\) 
real 

acceleration along y axis  4  
1302  variable 
\vec{p}_{\rm before}
\(\vec{p}_{\rm before}\) 
real 

momentum before collision  2  
5493  variable 
\vec{p}_{\rm after}
\(\vec{p}_{\rm after}\) 
real 

momentum after collision  3  
6029  variable 
\vec{p}_1
\(\vec{p}_1\) 
real 

momentum 1  5  
2097  variable 
\vec{p}_2
\(\vec{p}_2\) 
real 

momentum 2  5  
4299  variable 
\vec{p}_{\rm electron}
\(\vec{p}_{\rm electron}\) 
real 

momentum of electron  5  
7427  variable 
v_{\rm Earth\ orbit}
\(v_{\rm Earth\ orbit}\) 
real 

velocity of Earth's orbit around sun 

6  
5344  variable 
t_{\rm Earth\ orbit}
\(t_{\rm Earth\ orbit}\) 
real 

time of Earth's orbit around sun 

5  
8039  variable 
H
\(H\) 
real 

enthalpy  0  
5786  variable 
U
\(U\) 
real 

internal energy  7  
5480  variable 
\pi_T
\(\pi_T\) 
real 

internal pressure at constant temperature  2  
6682  variable 
C_V
\(C_V\) 
real 

heat capacity at constant volume  2  
9432  variable 
Q
\(Q\) 
real 

heat flow  1  
8134  variable 
P
\(P\) 
real 

pressure  13  
7586  variable 
V
\(V\) 
real 

volume  15  
9843  variable 
\mu_{JT}
\(\mu_{JT}\) 
real 

JouleThomson coefficient  0  
4686  variable 
\alpha
\(\alpha\) 
real 

expansion coefficient  6  
4610  variable 
\mu_T
\(\mu_T\) 
real 

isothermal JouleThomson coefficient  0  
1394  variable 
S
\(S\) 
real 

entropy  1  
3434  variable 
\Omega
\(\Omega\) 
real 

number of microscopic configurations (known as microstates) that are consistent with the macroscopic quantities that characterize the system  1  
7343  variable 
T
\(T\) 
real 

temperature  18  
4645  variable 
\kappa_T
\(\kappa_T\) 
real 

coefficient of isothermal compressibility 

6  
2834  variable 
n
\(n\) 
real 

amount of substance  8  
8179  constant 
R
\(R\) 
real 

ideal gas constant 
8.31446261815324 Jâ‹…K^{âˆ’1} mol^{âˆ’1} 
8  
7940  constant 
\epsilon_0
\(\epsilon_0\) 
real 

vacuum permittivity, permittivity of free space or electric constant or the distributed capacitance of the vacuum 
8.8541878128E{12} F/m 
14  
6197  constant 
\mu_0
\(\mu_0\) 
real 

vacuum permeability, permeability of free space, permeability of vacuum, or magnetic constant 
1.25663706212E^{6} N/A^2 
8  
9189  variable 
\omega_{\rm Debye}
\(\omega_{\rm Debye}\) 
real 

Debye frequency  0  
2851  variable 
k_{\rm Debye}
\(k_{\rm Debye}\) 
real 

Debye wavevector  0  
2875  constant 
r_{\rm Bohr}
\(r_{\rm Bohr}\) 
real 

Bohr radius 
5.29E^{11} m 
0  
5916  constant 
m_p
\(m_p\) 
real 

mass of proton 
1.67262192369E^{27} kg 
3  
2515  constant 
m_e
\(m_e\) 
real 

mass of electron 
9.1093837015E^{31} kg 
7  
9838  variable 
E_{\rm Rydberg}
\(E_{\rm Rydberg}\) 
real 

Rydberg energy  2  
9863  variable 
m
\(m\) 
real 

mass of atom or molecule  8  
5854  variable 
a
\(a\) 
real 

atomic separation 

5  
2241  variable 
E
\(E\) 
real 

bonding energy 

6  
3033  variable 
G
\(G\) 
real 

shear modulus  2  
1466  variable 
K
\(K\) 
real 

bulk modulus  2  
2077  variable 
v
\(v\) 
real 

longitudinal speed of sound in condensed matter  9  
3935  variable 
\rho
\(\rho\) 
real 

density  7  
4635  constant 
v_u
\(v_u\) 
real 

upper limit on velocity in condensed matter 
36100 m/s 
1  
6235  variable 
f
\(f\) 
real 

proportionality constant 

5  
3285  variable 
A
\(A\) 
real 

atomic mass  3  
2046  variable 
\vec{p}
\(\vec{p}\) 
real 

momentum  5  
7394  variable 
\vec{k}
\(\vec{k}\) 
real 

wavenumber  1  
9472  variable 
\vec{r}
\(\vec{r}\) 
real 

radius vector 

24  
7110  variable 
r_{\rm geostationary\ orbit}
\(r_{\rm geostationary\ orbit}\) 
real 

geostationary orbital radius  2  
4679  variable 
\langle \psi_{\alpha} 
\(\langle \psi_{\alpha} \) 
complex  dimensionless  bra  7  
2090  variable 
 \psi_{\beta} \rangle
\( \psi_{\beta} \rangle\) 
complex  dimensionless  ket  7  
2427  variable 
a_{\alpha}
\(a_{\alpha}\) 
complex  dimensionless  none  4  
7752  variable 
a_{\beta}
\(a_{\beta}\) 
complex  dimensionless  none  5  
4065  variable 
\langle \psi
\(\langle \psi\) 
complex  dimensionless  bra  4  
9329  variable 
\psi \rangle
\(\psi \rangle\) 
complex  dimensionless  ket  1  
6799  variable 
{\cal H}
\({\cal H}\) 
complex  dimensionless  operator  1  
3474  variable 
\epsilon
\(\epsilon\) 
real  dimensionless  LeviCivita  0  
9669  variable 
\delta
\(\delta\) 
real  dimensionless  Kronecker delta  0  
9489  variable 
\psi
\(\psi\) 
complex  dimensionless  none 

27  
5340  variable 
KE_{\rm final}
\(KE_{\rm final}\) 
real  dimensionless  final kinetic energy  5  
4121  variable 
KE_{\rm initial}
\(KE_{\rm initial}\) 
real  dimensionless  initial kinetic energy  5  
1934  variable 
v_{\rm initial}
\(v_{\rm initial}\) 
real 

initial velocity  4  
8909  variable 
v_{\rm final}
\(v_{\rm final}\) 
real 

final velocity  9  
5734  variable 
\Delta KE
\(\Delta KE\) 
real  dimensionless  change in kinetic energy  2  
6777  variable 
\vec{F}
\(\vec{F}\) 
real  dimensionless  force  1  
6191  variable 
W_{\rm by\ system}
\(W_{\rm by\ system}\) 
real 

work done by system  5  
9372  variable 
W_{\rm to\ system}
\(W_{\rm to\ system}\) 
real 

work done to system  8  
4326  variable 
\vec{E}
\(\vec{E}\) 
complex  dimensionless  electric field  9  
7984  variable 
i
\(i\) 
integer  dimensionless  index 

1  
9690  variable 
k
\(k\) 
integer  dimensionless  index 

4  
8304  variable 
l
\(l\) 
integer  dimensionless  index 

3  
7930  variable 
m
\(m\) 
integer  dimensionless  index 

5  
2423  variable 
\vec{a}
\(\vec{a}\) 
real 

acceleration 

2  
6373  variable 
\vec{v}
\(\vec{v}\) 
real 

velocity 

2  
5505  variable 
v_x
\(v_x\) 
real 

velocity along x axis 

7  
6238  variable 
E
\(E\) 
real  dimensionless  electric field  20  
2069  variable 
\vec{H}
\(\vec{H}\) 
real  dimensionless  magnetic field  3  
3981  variable 
h
\(h\) 
integer  dimensionless  index 

0  
8349  variable 
\hat{x}_i
\(\hat{x}_i\) 
real  dimensionless  ith unit vector 

3  
1434  variable 
\hat{x}_n
\(\hat{x}_n\) 
real  dimensionless  nth unit vector 

1  
2380  variable 
\hat{x}_m
\(\hat{x}_m\) 
real  dimensionless  mth unit vector 

1  
8330  variable 
\psi_0
\(\psi_0\) 
complex  dimensionless  amplitude of wavefunction 

6  
4183  variable 
F_{\rm{spring}}
\(F_{\rm{spring}}\) 
real 

force of a spring  1  
1356  variable 
k
\(k\) 
real 

linear stiffness, aka spring constant  7  
9885  variable 
A
\(A\) 
real  dimensionless  amplitude  4 
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