Physics GRE Equations Sheet Version 1.0 Contact:
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Contents 1 Cla Classic ssical al Mec Mechan hanics ics
1
2 Ele Electri ctricit city y & Magn Magneti etism sm
3
3 Op Opti tics cs
4
4 The Thermody rmodynam namics ics & Statistica Statisticall Mechanic Mechanicss
5
5 Qua Quant ntum um Mec Mechan hanics ics
7
6 Spec Special ial Rel Relati ativit vity y
8
7 Ele Elect ctron ronics ics
9
8 Spe Speci cial al Top opics ics
1
10
Clas Classi sica call Mec Mechani hanics cs
Equations Kinematics: 1 ∆x = v0 t + at2 2 2 2 v = v0 + 2ad v = +at v0 + vf ∆x = t
2
Newton’s Second Law: F = ma
Momentum: P = mv
Centripetal Acceleration: = ω 2r F = mrω 2 2π ω =
ac
T
1
1
Gravitational Potential Energy: U = mgh m1 m2 U = G R U = W
− −
Kinetic Energy: =
1 mv 2 2
U k
=
p2 2m
U k−rotational
=
U k
1 2 Iω 2
Parallel Axis Theorem: 2 I = I com com + M h
Work: W =
·
F s
Moment of Inertia (Point Mass): I = M R2
Schwarzschild Radius: Re =
2GM c2
Lagrangian: L = T
− V
Hamiltonian: H = T + V
Angular Frequency: ω ωSH O
= =
2π T
k m
Period of a SHO: T = 2π
2
m k
CLASSI CLASSICAL CAL MECHAN MECHANICS ICS
2
2
Elec Electr tric icit ity y & Magn Magnet etis ism m
Equations Maxwell’s Equations: ρ 0
· E · B × E
= 0
× B
+ µ0 0 = µ0 J
=
=
− ∂ ∂tB
∂ E ∂t
Coulombs Law: U = U = F =
1 dQ 4π0 R 1 q1 q2 4π0 R 1 q1 q2 4π0 R2
Hooke’s Law: F =
−kx
Faraday’s Law of Induction dφB ε = N dt
|| Magnetic Flux: φB =
( B r , t) dA
·
S
Malus’ Law: I =
1 c0 E 02 cos2 (θ ) 2
Gauss’ Law: dA = q E 0
·
Larmor Formula: P =
q 2 a2 6π0 c3
Lorentz Force:
×
F = q v
B
Hall Voltage: V H H =
3
IB − dne
ELECTR ELECTRICI ICITY TY & MAG MAGNET NETISM ISM
3
3
Optics
Equations Photoelectric Photoelectric Equation: Equation: U k = hν
−φ
Snell’s Law: sin(θ1 ) n2 = sin(θ2 ) n1 n-slit constructive interference: d sin(θn ) = nλ
n-slit destructive interference: 1 λ 2
d sin(θn ) =
n+
Photon Energy: E = hν hc E = λ
Interference of a thin film: 1 2nd = m + λ 2
Light speed through a medium: v=
1 µ
Traveling wave: y(x, t) = A sin
2π
λ
(x
± vt)
Drift velocity: velocity: vd =
i nqA
Compton Equation: Equation: λ
− λ = mh c (1 − cos(θ)) p
4
OPT PTIICS
4
4
THERMODY THERMODYNAMICS NAMICS & STA STATISTICAL TISTICAL MECHANICS MECHANICS
Thermody Thermodynam namics ics & Stati Statisti stica call Mec Mechanics hanics
Equations Rydberg Formula: 1 λ
= R∞
1
1
−n
n21
2 2
Rydberg Formula for Hydrogen like atoms: 1
2
λH −like
= RZ
1 n21
1
−n
2 2
Moseley’s Law: 1
= R (Z
λK −α
− β)
2
1
1
−n
n21
2 2
Rydberg Energy: E =
− m2¯he e
4
2
E = E 0
1
Z 2 n2
1
λ21
−λ
2
E = n(13.6 eV )
1
λ21
1
−λ
2 2
Heat Capacity: Capacity: C =
∆Q ∆T
∂Q ∂T ∂S C = T ∂T ∂Q C V V = ∂T ∂Q C p = ∂T C =
∂U ∂T ∂H ∂T
=
V
=
p
Heat: Q = cm∆T
First Law of Thermodynamics: dU = dQ + dW dU = dQ
− P dV
Ideal Gas Law: pV = nRT
Thermodynamic Work: W =
V f
V i
5
P dV
V
p
4
THERMODY THERMODYNAMICS NAMICS & STA STATISTICAL TISTICAL MECHANICS MECHANICS
Entropy: ∆S =
T 2
dq T
T 1
Fourier’s Law of Heat Conduction: ∂Q = ∂t
−
T dA
k
s
·
Mean free path: P (x) = nσdx
Stefan-Boltzmann’s Law: j ∗ = σT 4
6
5
5
Quan Quantu tum m Mec Mechani hanics cs
Equations Particle Particle Location (Probability (Probability): ): b
P ab ab =
|
ψ(x) 2 dx
|
a
Infinite Square Well/Particle in a box: ψn (x, t) = Asin(kn x)e−iωn t
Planck Planck Length: Length:
¯ Gh 3 c
l p =
Expectation Value:
A =
| |
ψ A ψ
Heisenberg Uncertainty Principle: ∆x∆ p
≥ h¯2
Spin Operator: S 12 ψ1 = S 1 (S 1 + 1)ψ1
Probability Current: ¯ (x, t) = h J 2mi
∂ψ ψ ∂x ∗
−
∂ψ ∗ ψ ∂x
Quantum Harmonic Oscillator 1 2
E n = ¯ hω n + hω
Wave Speed (de Broglie relations): v p
=
v p
=
E p c2 v
Time-Independent Schrodinger Equation: E ψ(x) =
¯2 h 2m
2
−
7
ψ (x) + V (x) ψ (x)
QUANTU QUANTUM M MECHAN MECHANICS ICS
6
6
Speci Special al Rela Relati tivi vitty
Equations Rest Energy: E = m0 c2
Lorentz Factor: γ =
1
−
v2 c2
1
Relativistic Relativistic Energy: E R = γmc 2
Relativistic Momentum: prel = γm 0 v =
m0 v
−
v2 c2
1
Relativistic Energy-Momentum:
E 2 = mc2
2
+ ( pc)2
Relativistic sum of velocities: u
=
u+v
1 + vu c u + v 1 + vcu 2
u =
2
Proper Time: ∆τ 2 = ∆t2
2
− ∆x
∆t2 = ∆τ 2 + ∆x2 Space-Time Interval: ∆S 2 =
2
−(C ∆t)
8
+ ∆x2
SPECIA SPECIAL L RELA RELATIVITY TIVITY
7
7
Elec Electr tron onic icss
Equations Ohm’s Law: V = I R
Kirchoff’s First Law: n
I = 0
k=1
Kirchoff’s Second Law: n
V = 0
k=1
Current: i=
dq dt
Faraday’s law of induction: dφB ε= dt
Capacitance
C =
Q V
Frequency of an RLC Circuit f =
9
1 √ 4π LC
ELEC ELECTR TRON ONIC ICS S
8
8
Speci Special al Topic opicss
Equations Acoustic Beats: beats = f 2
| − f | 1
Doppler Effect: f =
1 1
±
10
vs ource vw ave
f 0
SPEC SPECIA IAL L TOPI TOPICS CS
