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GRE Physics

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Answer 50 questions in 15 minutes.
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1. Quant: [L_x -L_y] = ?
ih_barL_z
Faraday/Lenz: current inducted opposes the changing field
PdV +dU
Braking Radiation

2. Source-free RC Circuit
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Isentropic
L = L_0 Sqrt[1-v^2/c^2]
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

3. Thermo: Isothermal
?s = 0 - ?l = ±1
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
dU = 0 ? dS = ?dW/T
P/A = s T^4

4. Thermo: 1st Law
Dv = -udm/m - v = v0 + u ln(m0/m)
v(mean)
dQ = dW +dU
E = s/e_0

5. Wein'S Displacement Law
1/ne - where n is charge carrier density
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
?max = 2.898 x 10 -³ / T
I = I_cm + md²

6. Helmholtz Free Energy
U - ts = -tlog(Z)
M? = 2dsin(?)
? exp(-e/t)
X_L = i?L

7. Energy in Inductor
.5 LI²
F = µ0 q v I / 2pr
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
? = 5/3

8. Rayleigh criterion
? exp(-e/t)
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
.5 CV²
? = 1.22? / d

9. Polarizers - intensity when crossed at ?
W_A < W_I
ma + kx = 0
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
I = I_0 Cos[?]^2

10. EM: Bremsstrahlung (translation)
S = k ln[O] ; dS = dQ/T
? = 5/3
Braking Radiation
µ = Current * Area T = µ x B

11. Magnetic field due to a segment of wire
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
A[B -C] + [A -C]B
L = T - V dL/dq = d/dt dL/dqdot
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point

12. Magnetic Field of a long solenoid
?max = 2.898 x 10 -³ / T
B = µ0 I n
ma + kx = 0
Always Real

13. Quant: Eigenvalue of Hermitian Operator
Always Real
F = f* (c+v_r)/(c+v_s)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
F = R/2

14. EM: Series Capacitance
C_eq = (? 1/C_i)^-1
Infinitely close to equilibrium at all times
Exponentially decreasing radial function
M? = 2dsin(?)

15. Bernoulli Equation
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
Sin(?) = ?/d
F = qv×B
P +1/2 ? v² + ?gh = Constant

16. Doppler shift for light
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
J = ? Fdt
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

17. Lab: Standard Deviation of Poisson
ih_barL_z
v(mean)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
<?1|?2> = 0 ? Orthogonal

18. De Broglie wavelength
1/vLC
µ=s^2
? = h/p
E = Z²*E1

19. Internal Energy of an Ideal Gas
(3/2) n R ?t
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Measurements close to true value
I ' = I cos²(?)

20. EM: Reactance of Capacitor
X_C = 1/(i?C)
µ = m_e/2
qvb = mv²/R
?_max = b/T

21. Relativistic Energy
?mc²
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
L = T - V dL/dq = d/dt dL/dqdot
U = t^2 d/dt (logZ)

22. Rocket Equation
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
Cos[?] Sin[?] -Sin[?] Cos[?]
U - ts = -tlog(Z)
Dv = -udm/m - v = v0 + u ln(m0/m)

23. Thermo: Monatomic gas ?=?
? = 5/3
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
ds² = (c*dt)² - ?(x_i)²
<?1|?2> = 0 ? Orthogonal

24. Atom: Bohr Theory Ionization
Infinitely close to equilibrium at all times
S = k ln[O] ; dS = dQ/T
Faraday/Lenz: current inducted opposes the changing field
E = Z²*E1

25. Focal point of mirrror with curvature
Infinitely close to equilibrium at all times
dQ = dW +dU
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
F = R/2

26. Kepler'S Three Laws
V(r) + L²2/2mr²
Int ( A . dr) = Int ( del x A) dSurface
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

27. Wein'S displacement law for blackbodies (? and T)
<?|O|?>
I = I_cm + md²
?_max = b/T
?s = 0 - ?l = ±1

28. Stark Effect
F = f* (c+v_r)/(c+v_s)
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
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

29. EM: SHO (Hooke)
ma + kx = 0
X_L = X_C or X_total = 0
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

30. td(entropy) =
µ0 I / 2R
PdV +dU
ds² = (c*dt)² - ?(x_i)²
Dv = -udm/m - v = v0 + u ln(m0/m)

31. Angular momentum - Central Force Motion
F = R/2
dU = 0 ? dS = ?dW/T
µ = m_e/2
L = mr²d?/dt

32. Lab: Precision of Measurements
Measurements close to mean
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Ct²-x²-y²-z²
I ' = I cos²(?)

33. Coriolis Force
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
T = I?²/2
F = -2*m(? x r)
I = I_0 Cos[?]^2

34. Angular momentum operators L^2 and L_z
W_A < W_I
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
<?|O|?>
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

35. Pauli matrices
P/A = s T^4
Int ( A . dr) = Int ( del x A) dSurface
PdV +dU
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

36. E field of a capacitor (d->0)
F = R/2
? exp(-e/t)
E = s/e_0
KE = 1/2 * µ (dr/dt)² L = µ r x v

37. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
? = h/p
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
I = I_cm + md²

38. Solid: Resistivity of Semi-Conductor
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
?~1/T
I_z = I_x + I_y (think hoop symmetry)
C_eq = (? 1/C_i)^-1

39. EM: Parallel Capacitance
C_eq = ?C_i
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
µ0 I1I2 / (2pd)
Braking Radiation

40. Lagrangian and Lagrange'S equation
L = T - V dL/dq = d/dt dL/dqdot
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Cos[?] Sin[?] -Sin[?] Cos[?]
µ0 I1I2 / (2pd)

41. Selection rules for atomic transitions
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
E = s/e_0
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
P² ~ R³

42. Error in the mean if each measurement has the same uncertainty s
(° of Freedom)kT/2
Infinitely close to equilibrium at all times
S_mean = s/Sqrt[N]
X_C = 1/(i?C)

43. Quant: Commutator Relation [AB -C]
µ = m_e/2
A[B -C] + [A -C]B
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
dQ = dW +dU

44. Resistance - length - area - rho
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
F = mv²/r
?_max = b/T
? exp(-e/t)

45. Law of Mass Action
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
T^2 = k R^3 - k=constant
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

46. Bohr Model: Radii
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
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
N²/Z (m_elec/m_red)
(° of Freedom)kT/2

47. Single Slit Diffraction Maximum
Asin(?) = m?
Hbar*?³/(p²c³exp(hbar?/t)-1)
? exp(-e/t)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

48. Current in resistor in RC circuit
I = V/R exp(-t/RC)
<?|O|?>
T = I?²/2
X_L = X_C or X_total = 0

49. Perturbations
0
H = H_0 + ?H
Exponentially decreasing radial function
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

50. Magnetic Dipole Moment and Torque
µ = Current * Area T = µ x B
B = µ0 I n
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

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