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GRE Physics

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. Doppler shift for light
? exp(-e/t)
Z_c = -i/(?C) ; Z_L = i ? L
? = ?_0 Sqrt[(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

2. Quant: [L_x -L_y] = ?
ih_barL_z
dQ = dW +dU
L = T - V dL/dq = d/dt dL/dqdot
Q = CVexp(-t/RC)

3. Rayleigh criterion
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
F_f = µ*F_N
E²-p²c²
? = 1.22? / d

4. EM: Reactance of Capacitor
X_C = 1/(i?C)
(° of Freedom)kT/2
F = R/2
? = ?0 root((1-v/c)/(1+v/c))

5. Atom: Orbital Config
J = ? Fdt
S_mean = s/Sqrt[N]
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
T^2 = k R^3 - k=constant

6. Addition of relativistic velocities

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7. Resistance - length - area - rho
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
?? = h/mc * (1-cos(?))
I = V/R exp(-t/RC)
V(r) + L²2/2mr²

8. Bohr Model: Energy
P +1/2 ? v² + ?gh = Constant
F = R/2
Z²/n² (m_red/m_elec)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

9. Gibbs Factor
µ = Current * Area T = µ x B
Sin(?) = ?/d
Braking Radiation
Exp(N(µ-e)/t)

10. Work (P - V)
?~T
X_L = X_C or X_total = 0
µ0 I / 2R
P1V1 - P2V2 / (? - 1)

11. Angular momentum operators L^2 and L_z
NC?T
?? = h/mc * (1-cos(?))
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
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

12. Single Slit Diffraction Maximum
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Asin(?) = m?
M? = 2dsin(?)

13. EM: Electromagnetic inertia
Always Real
E²-p²c²
Faraday/Lenz: current inducted opposes the changing field
C_eq = (? 1/C_i)^-1

14. Atom: Positronium Reduced Mass
V(r) + L²2/2mr²
(° of Freedom)kT/2
µ = m_e/2
P +1/2 ? v² + ?gh = Constant

15. Mech: Rotational Energy
T = I?²/2
<?|O|?>
F = f* (c+v_r)/(c+v_s)
KE = 1/2 * µ (dr/dt)² L = µ r x v

16. Complex impedance (expressions for capacitor and inductor)
u dm/dt
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
Z_c = -i/(?C) ; Z_L = i ? L
(° of Freedom)kT/2

17. Magnetic Field of a long solenoid
µ = m_e/2
F = qv×B
B = µ0 I n
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

18. Ohm'S Law w/ current density
µ0 I / 2pR
J = E s - s = Conductivity - E = Electric field
U = t^2 d/dt (logZ)
Dp/dt = L / (t ?V)

19. RLC resonance condition
V = -L di/dt
(° of Freedom)kT/2
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
L = T - V dL/dq = d/dt dL/dqdot

20. Adiabatic processes (dS - dQ - P and V)
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.
DS = 0 - dQ = 0 - P V^? = constant
ih_barL_z
I = -(c ?t)^2 + d^2

21. Thin Film Theory: Constructive / Destructive Interference
Const: 2t = (n +.5)? Destructive 2t = n?
?mv
L = L_0 Sqrt[1-v^2/c^2]
Measurements close to mean

22. Stark Effect
Measurements close to mean
0
KE = 1/2 * µ (dr/dt)² L = µ r x 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

23. Magnetic Field For Current in Long Wire
?~T
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
µ0 I / 2pR
X_L = i?L

24. QM: de Broglie Wavelength
µ = Current * Area T = µ x B
?= h/v(2mE)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
T = I?²/2

25. Lab: Standard Deviation of Poisson
<?1|?2> = 0 ? Orthogonal
PdV +dU
v(mean)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

26. Invariant Energy Quantity
?= h/v(2mE)
W_A < W_I
E²-p²c²
Braking Radiation

27. Energy in terms of partition function
Z²/n² (m_red/m_elec)
U = t^2 d/dt (logZ)
Sin(?) = ?/d
L = mr²d?/dt

28. Stoke'S Theorem
N²/Z (m_elec/m_red)
µ0 I / 2pR
dQ = dW +dU
Int ( A . dr) = Int ( del x A) dSurface

29. Rocket Thrust
E = <?| H |?>
Isentropic
P² ~ R³
u dm/dt

30. Internal Energy of an Ideal Gas
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Cv = dE/dT = 3R
(3/2) n R ?t
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.

31. Volumetric Expansion
1/vLC
Cos[?] Sin[?] -Sin[?] Cos[?]
V = V0 + V0 a ?T
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h

32. Wein'S displacement law for blackbodies (? and T)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Z = ?g_i*exp(-E/kT)
?_max = b/T
P1V1 - P2V2 / (? - 1)

33. Boltzmann / Canonical distribution
Asin(?) = m?
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
?_max = b/T
Dv = -udm/m - v = v0 + u ln(m0/m)

34. Thermo: Isothermal
dU = 0 ? dS = ?dW/T
L = T - V dL/dq = d/dt dL/dqdot
1/ne - where n is charge carrier density
V(r) + L²2/2mr²

35. Relativistic interval (which must remain constant for two events)
I = -(c ?t)^2 + d^2
H = H_0 + ?H
Hbar*?³/(p²c³exp(hbar?/t)-1)
F = f* (c+v_r)/(c+v_s)

36. EM: SHO (Hooke)
Measurements close to true value
ma + kx = 0
J/(ne) n: atom density
? = h/mv

37. Thermo: Blackbody Radiation
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
F = s * T4
?mc²
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

38. Kepler'S third law (T and R)
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
T^2 = k R^3 - k=constant
Hbar*?³/(p²c³exp(hbar?/t)-1)
Const: 2t = (n +.5)? Destructive 2t = n?

39. Source-free RC Circuit
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
.5 CV²
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
? = 1.22? / d

40. How to derive cylcotron frequency
v(mean)
qvb = mv²/R
V(r) + L²2/2mr²
L = T - V dL/dq = d/dt dL/dqdot

41. Compton Scattering
I = Im (sinc²(a)) ; a = pai sin(?) / ?
?? = h/mc * (1-cos(?))
Exponentially decreasing radial function
C_eq = (? 1/C_i)^-1

42. EM: Maxwell'S equations
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
P +1/2 ? v² + ?gh = Constant
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Always Real

43. E field of a capacitor (d->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
E = s/e_0
? = h/p
Exp(N(µ-e)/t)

44. Commutator identities ( [B -A C] - [A -B] )
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Q = CVexp(-t/RC)

45. Atom: Hydrogen Wave Function Type
Exponentially decreasing radial function
Const: 2t = (n +.5)? Destructive 2t = n?
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
X_C = 1/(i?C)

46. Energy in Inductor
P +1/2 ? v² + ?gh = Constant
.5 LI²
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.
L = mr²d?/dt

47. Weighted average (mean and unc. of mean)
E = s/e_0
NC?T
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

48. Relativistic Momentum
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
?mv

49. Planck Radiation Law
Hbar*?³/(p²c³exp(hbar?/t)-1)
qvb = mv²/R
V = -L di/dt
µ=s^2

50. EM: Series Capacitance
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
J/(ne) n: atom density
0
C_eq = (? 1/C_i)^-1