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GRE Physics

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1. Selection Rules
Measurements close to true value
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
?s = 0 - ?l = ±1
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

2. Work done on a gas
? = 1.22? / d
µ0 I1I2 / (2pd)
DW = P dV
L = T - V dL/dq = d/dt dL/dqdot

3. De Broglie wavelength
ma + kx = 0
? = h/p
? = 1.22?/D
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

4. Electromotive Force
PdV +dU
I = I_cm + (1/2)m d^2
DW/dq
E = Z²*E1

5. Time Lorentz Transformation
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
? (t-vx/c²)
Dp/dt = L / (t ?V)
Z = ?g_i*exp(-E/kT)

6. Lagrangian and Lagrange'S equation
v(mean)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
L = T - V dL/dq = d/dt dL/dqdot
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

7. Mech: Centripetal Force
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
F = mv²/r
H = H_0 + ?H
.5 CV²

8. Astro: Aperture Formula (Rayleigh Criterion)
? = 1.22?/D
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
U - ts = -tlog(Z)
I = -(c ?t)^2 + d^2

9. Source Free RL Circuit
Exp(N(µ-e)/t)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
(3/2) n R ?t
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

10. EM: AC Resonance
Cos[?] Sin[?] -Sin[?] Cos[?]
X_L = X_C or X_total = 0
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

11. EM: Reactance of Capacitor
1/2 CV²
X_C = 1/(i?C)
C = 4pe0 ab/(a-b) = inner and outer radii
S = k ln[O] ; dS = dQ/T

12. Lab: Standard Deviation of Poisson
v(mean)
P1V1 - P2V2 / (? - 1)
J = ? Fdt
S_mean = s/Sqrt[N]

13. Spherical Capacitor Equation
Const: 2t = (n +.5)? Destructive 2t = n?
C = 4pe0 ab/(a-b) = inner and outer radii
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
F = µ0 q v I / 2pr

14. Atom: Positronium Reduced Mass
µ = m_e/2
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Q = CVexp(-t/RC)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

15. Springs in series/parallel
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
V = -L di/dt
?s = 0 - ?l = ±1
F_f = µ*F_N

16. Doppler Shift for light
? = ?0 root((1-v/c)/(1+v/c))
X_L = X_C or X_total = 0
Q = CVexp(-t/RC)
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

17. Doppler Shift in Frequency
F = f* (c+v_r)/(c+v_s)
F = µ0 q v I / 2pr
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
I = -(c ?t)^2 + d^2

18. RLC resonance condition
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
X_L = i?L
? = 1.22? / d
U = t^2 d/dt (logZ)

19. Bohr Model: Energy
F = qv×B
Z²/n² (m_red/m_elec)
E = <?| H |?>
T = I?²/2

20. Virial Theorem
J = E s - s = Conductivity - E = Electric field
NC?T
<T> = 1/2 * <dV/dx>
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

21. EM: Parallel Capacitance
P² ~ R³
?_max = b/T
Z = ?g_i*exp(-E/kT)
C_eq = ?C_i

22. Magnetic Dipole Moment and Torque
Faraday/Lenz: current inducted opposes the changing field
µ = Current * Area T = µ x B
Cv = dE/dT = 3R
?= h/v(2mE)

23. Thermo: Average Total Energy
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
In Zeeman effect - the contribution of electron spin to total angular momentum means that it isn'T always three lines and they are not always equally spaced.
1/2 CV²
(° of Freedom)kT/2

24. Rayleigh'S Criterion
Sin(?) = ?/d
Braking Radiation
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
When you apply a uniform electric field - it induces a dipole moment and interacts with it - and that effect depends on |mj |. So if j is an integer - splits (asymmetrically) into j+1 levels - and if j is a half integer - splits (asymmetrically) into

25. Relativistic Momentum
µ0 I / 2pR
?mv
ma + kx = 0
? = 1.22? / d

26. Ohm'S Law w/ current density
J = E s - s = Conductivity - E = Electric field
C = 4pe0 ab/(a-b) = inner and outer radii
N d flux / dt
When you apply a uniform electric field - it induces a dipole moment and interacts with it - and that effect depends on |mj |. So if j is an integer - splits (asymmetrically) into j+1 levels - and if j is a half integer - splits (asymmetrically) into

27. A reversible process stays..
U - ts = -tlog(Z)
E = <?| H |?>
Infinitely close to equilibrium at all times
T = I?²/2

28. Malus Law

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29. Bohr Model: Radii
N²/Z (m_elec/m_red)
(° of Freedom)kT/2
.5 CV²
I = -(c ?t)^2 + d^2

30. Stoke'S Theorem
µ = m_e/2
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
F = mv²/r
Int ( A . dr) = Int ( del x A) dSurface

31. EM: Series Capacitance
Cos[?] Sin[?] -Sin[?] Cos[?]
C_eq = (? 1/C_i)^-1
E = s/e_0
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

32. Focal point of mirrror with curvature
µ = Current * Area T = µ x B
F = R/2
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Int ( A . dr) = Int ( del x A) dSurface

33. Atom: Bohr Theory Ionization
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
I = I_cm + (1/2)m d^2
E = Z²*E1

34. Rocket Equation
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Dv = -udm/m - v = v0 + u ln(m0/m)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

35. Astro: p-p Chain
J = E s - s = Conductivity - E = Electric field
v(mean)
J/(ne) n: atom density
4H + 2e- ? He +2? + 6?

36. Invariant spatial quantity
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
L = T - V dL/dq = d/dt dL/dqdot
Exponentially decreasing radial function
Ct²-x²-y²-z²

37. Clausius-Clapeyron Equation
1/2 CV²
Dp/dt = L / (t ?V)
J = ? Fdt
?_max = b/T

38. Thermo: 1st Law
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Z²/n² (m_red/m_elec)
dQ = dW +dU
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

39. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
I = -(c ?t)^2 + d^2
A[B -C] + [A -C]B
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

40. Lensmaker Equation - Thin Lens
J = ? Fdt
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
(3/2) n R ?t
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave

41. Kepler'S third law (T and R)
<?|O|?>
I = I_cm + md²
<T> = 1/2 * <dV/dx>
T^2 = k R^3 - k=constant

42. Rayleigh criterion
? = 1.22? / d
Always Real
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
?~T

43. Single Slit Diffraction Intensity
Infinitely close to equilibrium at all times
Ct²-x²-y²-z²
I = Im (sinc²(a)) ; a = pai sin(?) / ?
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

44. EM: Electric Field inside of Conductor
µ0 I1I2 / (2pd)
I_z = I_x + I_y (think hoop symmetry)
0
Q = CVexp(-t/RC)

45. Kepler'S Three Laws
ih_barL_z
? = h/mv
(° of Freedom)kT/2
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

46. Atom: Orbital Config
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
?~1/T
F = s * T4
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

47. Triplet/singlet states: symmetry and net spin
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
µ = Current * Area T = µ x B
S = (hbar/2) s ;with S = S_x xhat + S_y yhat + S_z zhat -s = s_x xhat + s_y yhat + s_z zhat

48. Mech: Impulse
J = ? Fdt
T^2 = k R^3 - k=constant
Faraday/Lenz: current inducted opposes the changing field
Cos[?] Sin[?] -Sin[?] Cos[?]

49. Force exerted on charge by long wire
Cos[?] Sin[?] -Sin[?] Cos[?]
Ct²-x²-y²-z²
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
F = µ0 q v I / 2pr

50. SR: Total Energy of a Particle
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
I = -(c ?t)^2 + d^2
I_z = I_x + I_y (think hoop symmetry)
Asin(?) = m?

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