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GRE Physics

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Answer 50 questions in 15 minutes.
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1. Hamiltonian and Hamilton'S equations
Opposing charge induced upon conductor
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
J = ? Fdt
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

2. Pauli matrices
?~1/T
?? = h/mc * (1-cos(?))
F = -2*m(? x r)
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

3. Effective Potential
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
(3/2) n R ?t
I_z = I_x + I_y (think hoop symmetry)
V(r) + L²2/2mr²

4. EM: Electric Field inside of Conductor
0
Faraday/Lenz: current inducted opposes the changing field
Asin(?) = m?
I = I_cm + (1/2)m d^2

5. Spherical Capacitor Equation
F = I L X B
C = 4pe0 ab/(a-b) = inner and outer radii
?mv
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

6. Center of Mass: Kinetic Energy & Angular Momentum
KE = 1/2 * µ (dr/dt)² L = µ r x v
? = h/p
1/ne - where n is charge carrier density
0

7. Weighted average (mean and unc. of mean)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
?~1/T
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

8. Selection rules for atomic transitions
qvb = mv²/R
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
W' = (w-v)/(1-w v/c^2) ; observer in S sees an object moving at velocity w; another frame S' moves at v wrt S.
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

9. Poisson distribution (µ and s)
µ=s^2
A[B -C] + [A -C]B
?s = 0 - ?l = ±1
Const: 2t = (n +.5)? Destructive 2t = n?

10. Gibbs Factor
Exp(N(µ-e)/t)
0
Measurements close to true value
I = Im (sinc²(a)) ; a = pai sin(?) / ?

11. Inductance of Solenoid
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
T = I?²/2
µ=s^2

12. Solid: Resistivity of Metal
? = ?0 root((1-v/c)/(1+v/c))
?~T
I = V/R exp(-t/RC)
ih_barL_z

13. Radiation (Larmor - and another neat fact)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
X_L = i?L
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
U = t^2 d/dt (logZ)

14. Clausius-Clapeyron Equation
F = f* (c+v_r)/(c+v_s)
Dp/dt = L / (t ?V)
V = V0 + V0 a ?T
F = s * T4

15. Relativistic Momentum
Measurements close to true value
F = mv²/r
Asin(?) = m?
?mv

16. Work in a capacitor
1/2 CV²
I = I_0 Cos[?]^2
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
B = µ0 I n

17. Wein'S Displacement Law
ih_barL_z
?max = 2.898 x 10 -³ / T
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
qvb = mv²/R

18. Angular momentum - Central Force Motion
I = I_0 Cos[?]^2
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
µ = m_e/2
L = mr²d?/dt

19. Biot-Savart law
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
P² ~ R³
? = h/mv
Braking Radiation

20. Angular momentum operators L^2 and L_z
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
C_eq = (? 1/C_i)^-1
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Const: 2t = (n +.5)? Destructive 2t = n?

21. Compton Scattering
Q = CVexp(-t/RC)
?? = h/mc * (1-cos(?))
Asin(?) = m?
dU = 0 ? dS = ?dW/T

22. Stoke'S Theorem
Measurements close to mean
1/vLC
Int ( A . dr) = Int ( del x A) dSurface
J = E s - s = Conductivity - E = Electric field

23. Mean electron drift speed
W_A < W_I
<T> = 1/2 * <dV/dx>
J/(ne) n: atom density
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

24. Magnetic Dipole Moment and Torque
F = mv²/r
1/ne - where n is charge carrier density
µ = Current * Area T = µ x B
Z²/n² (m_red/m_elec)

25. EM: SHO (Hooke)
? = 5/3
ma + kx = 0
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
E = Z²*E1

26. Induced EMF of solenoid
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
Z_c = -i/(?C) ; Z_L = i ? L
N d flux / dt

27. Law of Mass Action
F = f* (c+v_r)/(c+v_s)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
? = 1.22?/D
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))

28. Rocket Equation
Ct²-x²-y²-z²
ds² = (c*dt)² - ?(x_i)²
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
Dv = -udm/m - v = v0 + u ln(m0/m)

29. EM: Reactance of Capacitor
C_eq = (? 1/C_i)^-1
ih_barL_z
X_L = i?L
X_C = 1/(i?C)

30. Adiabatic processes (dS - dQ - P and V)
DS = 0 - dQ = 0 - P V^? = constant
F = I L X B
Const: 2t = (n +.5)? Destructive 2t = n?
? (t-vx/c²)

31. QM: de Broglie Wavelength
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
F = s * T4
?= h/v(2mE)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

32. Time Lorentz Transformation
?? = h/mc * (1-cos(?))
NC?T
? (t-vx/c²)
Asin(?) = m?

33. Anomalous Zeeman Effect

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34. De Broglie wavelength
?_max = b/T
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
µ0 I / 2R
? = h/p

35. Error in the mean if each measurement has the same uncertainty s
DS = 0 - dQ = 0 - P V^? = constant
X_C = 1/(i?C)
F = -2*m(? x r)
S_mean = s/Sqrt[N]

36. Charge in Capacitor
Q = CVexp(-t/RC)
µ0 I / 2pR
?s = 0 - ?l = ±1
Cv = dE/dT = 3R

37. Self Inductance
V = -L di/dt
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
<T> = -<V>/2
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

38. Astro: Kepler'S Third Law
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
I = I_0 Cos[?]^2
? = h/p
P² ~ R³

39. EM: Reactance of Inductor
Const: 2t = (n +.5)? Destructive 2t = n?
L = T - V dL/dq = d/dt dL/dqdot
X_L = i?L
F = I L X B

40. Bar magnets -- direction of B field lines - earth'S B field
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
? = ?0 root((1-v/c)/(1+v/c))

41. Atom: Orbital Config
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
F = µ0 q v I / 2pr
C_eq = ?C_i

42. Kepler'S Three Laws
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
PdV +dU
M? = 2dsin(?)
V(r) + L²2/2mr²

43. Selection Rules
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
?s = 0 - ?l = ±1
? = h/p
J/(ne) n: atom density

44. Thermo: Average Total Energy
Hbar*?³/(p²c³exp(hbar?/t)-1)
(° of Freedom)kT/2
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
F = -2*m(? x r)

45. Force on a wire in magnetic field
F = I L X B
P1V1 - P2V2 / (? - 1)
I = I_cm + md²
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

46. Bohr Model: Energy
4H + 2e- ? He +2? + 6?
?= h/v(2mE)
J = E s - s = Conductivity - E = Electric field
Z²/n² (m_red/m_elec)

47. EM: Maxwell'S equations
?? = h/mc * (1-cos(?))
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
1/ne - where n is charge carrier density
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

48. Atom: Positronium Reduced Mass
µ = m_e/2
Cv = dE/dT = 3R
1/2 CV²
X_L = X_C or X_total = 0

49. Atom: Bohr Theory Ionization
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
µ = m_e/2
?= h/v(2mE)
E = Z²*E1

50. A reversible process stays..
? = h/p
Infinitely close to equilibrium at all times
NC?T
U = t^2 d/dt (logZ)

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