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GRE Physics

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Answer 50 questions in 15 minutes.
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1. Thermo: Isothermal
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
F = f* (c+v_r)/(c+v_s)
dU = 0 ? dS = ?dW/T
I = Im (sinc²(a)) ; a = pai sin(?) / ?

2. Energy in terms of partition function
I_z = I_x + I_y (think hoop symmetry)
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
U = t^2 d/dt (logZ)
DS = 0 - dQ = 0 - P V^? = constant

3. Gibbs Factor
Exp(N(µ-e)/t)
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Measurements close to mean
Int ( A . dr) = Int ( del x A) dSurface

4. Thin Film Theory: Constructive / Destructive Interference
F = mv²/r
V = -L di/dt
Const: 2t = (n +.5)? Destructive 2t = n?
N²/Z (m_elec/m_red)

5. Focal point of mirrror with curvature
X_C = 1/(i?C)
M? = 2dsin(?)
F = R/2
ma + kx = 0

6. Ohm'S Law w/ current density
? = ?0 root((1-v/c)/(1+v/c))
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
?mc²
J = E s - s = Conductivity - E = Electric field

7. Doppler shift for light
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
DW = P dV
µ = m_e/2

8. EM: Bremsstrahlung (translation)
Asin(?) = m?
I = I_cm + md²
?~1/T
Braking Radiation

9. Quant: Expectation Value
J/(ne) n: atom density
1/ne - where n is charge carrier density
J = ? Fdt
<?|O|?>

10. Bohr Model: Radii
J = ? Fdt
Sin(?) = ?/d
Z_c = -i/(?C) ; Z_L = i ? L
N²/Z (m_elec/m_red)

11. Solid: Resistivity of Semi-Conductor
µ=s^2
Z²/n² (m_red/m_elec)
(° of Freedom)kT/2
?~1/T

12. Commutator identities ( [B -A C] - [A -B] )
µ=s^2
1/2 CV²
F = qv×B
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

13. EM: Reactance of Inductor
ma + kx = 0
NC?T
µ = Current * Area T = µ x B
X_L = i?L

14. Volumetric Expansion
1/vLC
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
V = V0 + V0 a ?T
?mc²

15. Internal Energy of an Ideal Gas
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
ds² = (c*dt)² - ?(x_i)²
(3/2) n R ?t
I_z = I_x + I_y (think hoop symmetry)

16. Solid: Resistivity of Metal
dQ = dW +dU
Exponentially decreasing radial function
Always Real
?~T

17. Wein'S Displacement Law
.5 CV²
?max = 2.898 x 10 -³ / T
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
E = <?| H |?>

18. Rayleigh'S Criterion
E²-p²c²
<?1|?2> = 0 ? Orthogonal
Sin(?) = ?/d
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

19. Astro: Aperture Formula (Rayleigh Criterion)
? = 1.22?/D
F = s * T4
Const: 2t = (n +.5)? Destructive 2t = n?
J/(ne) n: atom density

20. Thermo: Monatomic gas ?=?
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Braking Radiation
dU = 0 ? dS = ?dW/T
? = 5/3

21. Springs in series/parallel
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
µ0 I / 2R
ih_barL_z
DS = 0 - dQ = 0 - P V^? = constant

22. Expectation value of the energy of state |?>
µ0 I1I2 / (2pd)
?s = 0 - ?l = ±1
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
E = <?| H |?>

23. Parallel axis theorem
?max = 2.898 x 10 -³ / T
qvb = mv²/R
I = I_cm + (1/2)m d^2
Sin(?) = ?/d

24. Triplet/singlet states: symmetry and net spin
X_C = 1/(i?C)
ds² = (c*dt)² - ?(x_i)²
J = ? Fdt
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

25. Charge in Capacitor
Q = CVexp(-t/RC)
DW = P dV
C = 4pe0 ab/(a-b) = inner and outer radii
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

26. Perpendicular axis theorem
I_z = I_x + I_y (think hoop symmetry)
F = mv²/r
? exp(-e/t)
X_C = 1/(i?C)

27. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
E = s/e_0
N d flux / dt
ma + kx = 0

28. EM: Method of Images
Opposing charge induced upon conductor
1/2 CV²
? = 1.22?/D
µ=s^2

29. Thermo: Blackbody Radiation
L = mr²d?/dt
F = s * T4
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
µ0 I / 2R

30. Selection rules for atomic transitions
? = 1.22?/D
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
I ' = I cos²(?)
u dm/dt

31. Lab: Precision of Measurements
Cos[?] Sin[?] -Sin[?] Cos[?]
<?|O|?>
F = qv×B
Measurements close to mean

32. Planck Radiation Law
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
J = E s - s = Conductivity - E = Electric field
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
Hbar*?³/(p²c³exp(hbar?/t)-1)

33. EM: SHO (Hooke)
Asin(?) = m?
Cv = dE/dT = 3R
ma + kx = 0
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

34. Adiabatic processes (dS - dQ - P and V)
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
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
DS = 0 - dQ = 0 - P V^? = constant
v(mean)

35. Astro: p-p Chain
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
? = h/mv
4H + 2e- ? He +2? + 6?
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

36. SR: Total Energy of a Particle
DW = P dV
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Exp(N(µ-e)/t)
I = Im (sinc²(a)) ; a = pai sin(?) / ?

37. Bernoulli Equation
V = -L di/dt
E = <?| H |?>
P +1/2 ? v² + ?gh = Constant
Always Real

38. Clausius-Clapeyron Equation
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
(° of Freedom)kT/2
Dp/dt = L / (t ?V)
µ = Current * Area T = µ x B

39. Force/length between two wires
I = Im (sinc²(a)) ; a = pai sin(?) / ?
µ0 I1I2 / (2pd)
Braking Radiation
Cos[?] Sin[?] -Sin[?] Cos[?]

40. Energy in a Capacitor
Measurements close to true value
C_eq = (? 1/C_i)^-1
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
.5 CV²

41. De Broigle Wavelength
Dp/dt = L / (t ?V)
? = h/mv
T^2 = k R^3 - k=constant
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

42. Effective Potential
V(r) + L²2/2mr²
C = 4pe0 ab/(a-b) = inner and outer radii
Always Real
Dv = -udm/m - v = v0 + u ln(m0/m)

43. Addition of relativistic velocities

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44. Relativistic length contraction
U - ts = -tlog(Z)
L = L_0 Sqrt[1-v^2/c^2]
I ' = I cos²(?)
<T> = 1/2 * <dV/dx>

45. Lensmaker Equation - Thin Lens
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
v(mean)
Dv = -udm/m - v = v0 + u ln(m0/m)
Exponentially decreasing radial function

46. Quant: Commutator Relation [AB -C]
A[B -C] + [A -C]B
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
S_mean = s/Sqrt[N]
J = E s - s = Conductivity - E = Electric field

47. Delta Function Potential - type of WF
<?1|?2> = 0 ? Orthogonal
F = I L X B
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

48. Lab: Standard Deviation of Poisson
v(mean)
X_L = i?L
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
1/vLC

49. EM: Electric Field inside of Conductor
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
S_mean = s/Sqrt[N]
C_eq = (? 1/C_i)^-1
0

50. Doppler Shift for light
X_L = i?L
? = ?0 root((1-v/c)/(1+v/c))
µ0 I / 2pR
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

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