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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. Selection Rules
?= h/v(2mE)
?s = 0 - ?l = ±1
DW/dq
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

2. Energy in terms of partition function
L = T - V dL/dq = d/dt dL/dqdot
µ0 I / 2pR
U = t^2 d/dt (logZ)
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.

3. Doppler Shift in Frequency
F = f* (c+v_r)/(c+v_s)
qvb = mv²/R
Cv = dE/dT = 3R
?? = h/mc * (1-cos(?))

4. Astro: Aperture Formula (Rayleigh Criterion)
J/(ne) n: atom density
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
P1V1 - P2V2 / (? - 1)
? = 1.22?/D

5. Relativistic length contraction
N d flux / dt
L = L_0 Sqrt[1-v^2/c^2]
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
V = V0 + V0 a ?T

6. Commutator identities ( [B -A C] - [A -B] )
I = -(c ?t)^2 + d^2
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
Measurements close to mean
µ = Current * Area T = µ x B

7. How to derive cylcotron frequency
u dm/dt
I = I_cm + md²
qvb = mv²/R
Asin(?) = m?

8. Quant: Eigenvalue of Hermitian Operator
Always Real
?mc²
I_z = I_x + I_y (think hoop symmetry)
T^2 = k R^3 - k=constant

9. 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/ne - where n is charge carrier density
?s = 0 - ?l = ±1
L = mr²d?/dt

10. Effective Potential
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.
? = ?0 root((1-v/c)/(1+v/c))
Infinitely close to equilibrium at all times
V(r) + L²2/2mr²

11. Lab: Precision of Measurements
Measurements close to mean
Exp(N(µ-e)/t)
N d flux / dt
F = -2*m(? x r)

12. Perpendicular axis theorem
I = I_cm + (1/2)m d^2
I_z = I_x + I_y (think hoop symmetry)
S = k ln[O] ; dS = dQ/T
F = I L X B

13. Stefan-Boltzmann law for blackbodies (power per area and T)
1/ne - where n is charge carrier density
P/A = s T^4
µ0 I / 2pR
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

14. Resonance frequency of LC circuit
Asin(?) = m?
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
<T> = -<V>/2
1/vLC

15. Kepler'S Three Laws
Measurements close to mean
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
I_z = I_x + I_y (think hoop symmetry)

16. EM: AC Resonance
Cv = dE/dT = 3R
X_L = X_C or X_total = 0
Dv = -udm/m - v = v0 + u ln(m0/m)
.5 LI²

17. Wein'S displacement law for blackbodies (? and T)
Measurements close to mean
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
?_max = b/T
Braking Radiation

18. Source Free RL Circuit
S = k ln[O] ; dS = dQ/T
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
P +1/2 ? v² + ?gh = Constant
F = mv²/r

19. EM: Series Capacitance
KE = 1/2 * µ (dr/dt)² L = µ r x 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.
C_eq = (? 1/C_i)^-1
1/ne - where n is charge carrier density

20. Hall Coefficient
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
Z = ?g_i*exp(-E/kT)
1/ne - where n is charge carrier density
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

21. Biot-Savart law
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
L = L_0 Sqrt[1-v^2/c^2]
1/vLC
F = R/2

22. SR: Total Energy of a Particle
Infinitely close to equilibrium at all times
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
1/ne - where n is charge carrier density
?s = 0 - ?l = ±1

23. Stark Effect
I = Im (sinc²(a)) ; a = pai sin(?) / ?
U - ts = -tlog(Z)
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
? exp(-e/t)

24. Angular momentum operators L^2 and L_z
u dm/dt
PdV +dU
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

25. Gibbs Factor
4H + 2e- ? He +2? + 6?
dU = 0 ? dS = ?dW/T
Exp(N(µ-e)/t)
qvb = mv²/R

26. De Broigle Wavelength
? = h/mv
W_A < W_I
Const: 2t = (n +.5)? Destructive 2t = n?
Z = ?g_i*exp(-E/kT)

27. Self Inductance
U = t^2 d/dt (logZ)
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.
Dp/dt = L / (t ?V)
V = -L di/dt

28. Bernoulli Equation
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
J = E s - s = Conductivity - E = Electric field
Measurements close to mean
P +1/2 ? v² + ?gh = Constant

29. Selection rules for atomic transitions
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
<T> = 1/2 * <dV/dx>
I = I_cm + md²

30. Anomalous Zeeman Effect

31. Work (P - V)
P1V1 - P2V2 / (? - 1)
Cv = dE/dT = 3R
1/2 CV²
I ' = I cos²(?)

32. Magnetic Field of a long solenoid
I = I_cm + (1/2)m d^2
P/A = s T^4
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
B = µ0 I n

33. Springs in series/parallel
4H + 2e- ? He +2? + 6?
<T> = -<V>/2
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Infinitely close to equilibrium at all times

34. Bar magnets -- direction of B field lines - earth'S B field
.5 LI²
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
<T> = -<V>/2
J = E s - s = Conductivity - E = Electric field

35. Internal Energy of an Ideal Gas
?s = 0 - ?l = ±1
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.
L = mr²d?/dt
(3/2) n R ?t

36. Rayleigh'S Criterion
Sin(?) = ?/d
F = I L X B
C_eq = (? 1/C_i)^-1
Exp(N(µ-e)/t)

37. Radiation (Larmor - and another neat fact)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
S_mean = s/Sqrt[N]
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
?mc²

38. Atom: Bohr Theory Ionization
NC?T
Cos[?] Sin[?] -Sin[?] Cos[?]
E = Z²*E1
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

39. Entropy (# of states - and in terms of other thermo quantities)
Z = ?g_i*exp(-E/kT)
S = k ln[O] ; dS = dQ/T
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
0

40. Bohr Model: Radii
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
F = R/2
N²/Z (m_elec/m_red)
X_C = 1/(i?C)

41. Work done on a gas
DW = P dV
P1V1 - P2V2 / (? - 1)
F = f* (c+v_r)/(c+v_s)
F_f = µ*F_N

42. Polarizers - intensity when crossed at ?
Dp/dt = L / (t ?V)
E²-p²c²
I = I_0 Cos[?]^2
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

43. Rayleigh criterion
? = 1.22? / d
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
Z²/n² (m_red/m_elec)
ih_barL_z

44. Invariant spatial quantity
Ct²-x²-y²-z²
X_L = i?L
Cos[?] Sin[?] -Sin[?] Cos[?]
µ0 I / 2R

45. De Broglie wavelength
F = mv²/r
ma + kx = 0
L = L_0 Sqrt[1-v^2/c^2]
? = h/p

46. Energy levels from the Coulomb potential
I = -(c ?t)^2 + d^2
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
E = s/e_0
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

47. Time Lorentz Transformation
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
? (t-vx/c²)
Z = ?g_i*exp(-E/kT)
E²-p²c²

48. Dulong Petit Law
? exp(-e/t)
Cv = dE/dT = 3R
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
C = 4pe0 ab/(a-b) = inner and outer radii

49. Wein'S Displacement Law
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.
Braking Radiation
.5 CV²
?max = 2.898 x 10 -³ / T

50. Bragg'S Law of Reflection
Opposing charge induced upon conductor
µ0 I / 2pR
M? = 2dsin(?)
?~1/T