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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. Astro: p-p Chain
4H + 2e- ? He +2? + 6?
ma + kx = 0
Infinitely close to equilibrium at all times
I_z = I_x + I_y (think hoop symmetry)

2. Partition Function
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 = µ N² A / l : N = number of turns - A = cross sectional area -l = length
µ = m_e/2
? exp(-e/t)

3. Gibbs Factor
C_eq = ?C_i
Exp(N(µ-e)/t)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
F = f* (c+v_r)/(c+v_s)

4. Kepler'S third law (T and R)
Infinitely close to equilibrium at all times
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
F = R/2
T^2 = k R^3 - k=constant

5. Rayleigh criterion
F = -2*m(? x r)
? = 1.22? / d
v(mean)
qvb = mv²/R

6. Lab: Standard Deviation of Poisson
L = T - V dL/dq = d/dt dL/dqdot
E²-p²c²
v(mean)
S = k ln[O] ; dS = dQ/T

7. Delta Function Potential - type of WF
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
<T> = 1/2 * <dV/dx>
ds² = (c*dt)² - ?(x_i)²

8. SR: Spacetime Interval
Exp(N(µ-e)/t)
ds² = (c*dt)² - ?(x_i)²
F = µ0 q v I / 2pr
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

9. Resonance frequency of LC circuit
Measurements close to mean
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.
ma + kx = 0
1/vLC

10. Mech: Parallel Axis Theorem (Moment of Inertia)
I = I_cm + md²
µ0 I / 2pR
Braking Radiation
Z²/n² (m_red/m_elec)

11. Bohr Model: Energy
Z²/n² (m_red/m_elec)
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
I_z = I_x + I_y (think hoop symmetry)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

12. Quant: Orthogonality of States
<?1|?2> = 0 ? Orthogonal
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
L = T - V dL/dq = d/dt dL/dqdot
Hbar*?³/(p²c³exp(hbar?/t)-1)

13. Rocket Equation
F = qv×B
ds² = (c*dt)² - ?(x_i)²
Dv = -udm/m - v = v0 + u ln(m0/m)
Faraday/Lenz: current inducted opposes the changing field

14. Thermo: Adiabatic Work vs Isothermal Work
W_A < W_I
?= h/v(2mE)
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
X_L = X_C or X_total = 0

15. Relativistic interval (which must remain constant for two events)
Opposing charge induced upon conductor
µ = Current * Area T = µ x B
I = -(c ?t)^2 + d^2
ma + kx = 0

16. Astro: Kepler'S Third Law
P² ~ R³
I = I_cm + (1/2)m d^2
.5 CV²
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

17. Force on a wire in magnetic field
F_f = µ*F_N
F = I L X B
F = mv²/r
P² ~ R³

18. Thermo: Average Total Energy
? (t-vx/c²)
qvb = mv²/R
<?1|?2> = 0 ? Orthogonal
(° of Freedom)kT/2

19. Spherical Capacitor Equation
C = 4pe0 ab/(a-b) = inner and outer radii
4H + 2e- ? He +2? + 6?
?_max = b/T
I = V/R exp(-t/RC)

20. Angular momentum - Central Force Motion
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
ih_barL_z
L = mr²d?/dt
J/(ne) n: atom density

21. Source-free RC Circuit
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
Exp(N(µ-e)/t)
F_f = µ*F_N
I = -(c ?t)^2 + d^2

22. Double Slit: Interference Minimum - Diffraction Minimum
?s = 0 - ?l = ±1
X_L = X_C or X_total = 0
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
C = 4pe0 ab/(a-b) = inner and outer radii

23. SR: Total Energy of a Particle
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Infinitely close to equilibrium at all times
?mc²

24. Quant: Eigenvalue of Hermitian Operator
M? = 2dsin(?)
E = <?| H |?>
Always Real
<?|O|?>

25. Clausius-Clapeyron Equation
Q = CVexp(-t/RC)
Dp/dt = L / (t ?V)
F = f* (c+v_r)/(c+v_s)
<?|O|?>

26. Invariant spatial quantity
Ct²-x²-y²-z²
?? = h/mc * (1-cos(?))
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
? = h/mv

27. Weighted average (mean and unc. of mean)
(° of Freedom)kT/2
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
F = I L X B
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

28. Coriolis Force
µ0 I / 2R
F = -2*m(? x r)
Ct²-x²-y²-z²
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i

29. Magnetic Field Through Ring
J = ? Fdt
V = V0 + V0 a ?T
µ0 I / 2R
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

30. Relativistic length contraction
L = L_0 Sqrt[1-v^2/c^2]
Q = CVexp(-t/RC)
B = µ0 I n
P/A = s T^4

31. Thermo: Monatomic gas ?=?
? = 5/3
Opposing charge induced upon conductor
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.
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

32. Quant: [L_x -L_y] = ?
U = t^2 d/dt (logZ)
S_mean = s/Sqrt[N]
.5 CV²
ih_barL_z

33. Work done on a gas
DW = P dV
dU = 0 ? dS = ?dW/T
C_eq = ?C_i
Always Real

34. Lab: Precision of Measurements
I = Im (sinc²(a)) ; a = pai sin(?) / ?
(° of Freedom)kT/2
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Measurements close to mean

35. E field of a capacitor (d->0)
E = s/e_0
ds² = (c*dt)² - ?(x_i)²
(° of Freedom)kT/2
I = I_cm + (1/2)m d^2

36. Energy in Inductor
Int ( A . dr) = Int ( del x A) dSurface
.5 LI²
T = I?²/2
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length

37. Kepler'S Three Laws
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
dU = 0 ? dS = ?dW/T
U = t^2 d/dt (logZ)
? = 1.22?/D

38. Stoke'S Theorem
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
Int ( A . dr) = Int ( del x A) dSurface
E²-p²c²
F_f = µ*F_N

39. Adiabatic processes (dS - dQ - P and V)
Measurements close to true value
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
DS = 0 - dQ = 0 - P V^? = constant
E²-p²c²

40. Thin Film Theory: Constructive / Destructive Interference
Cos[?] Sin[?] -Sin[?] Cos[?]
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
U - ts = -tlog(Z)
Const: 2t = (n +.5)? Destructive 2t = n?

41. Poisson distribution (µ and s)
<?|O|?>
µ=s^2
Always Real
<T> = 1/2 * <dV/dx>

42. Atom: Hydrogen Wave Function Type
Exponentially decreasing radial function
Exp(N(µ-e)/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.
qvb = mv²/R

43. Mech: Rotational Energy
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
T = I?²/2
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
ih_barL_z

44. EM: AC Resonance
Always Real
F = -2*m(? x r)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
X_L = X_C or X_total = 0

45. Stark Effect
? = ?0 root((1-v/c)/(1+v/c))
<T> = -<V>/2
ih_barL_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

46. Mech: Force of Friction
Hbar*?³/(p²c³exp(hbar?/t)-1)
PdV +dU
F_f = µ*F_N
u dm/dt

47. Magnetic field due to a segment of wire
Int ( A . dr) = Int ( del x A) dSurface
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
L = mr²d?/dt
Always Real

48. Polarizers - intensity when crossed at ?
Isentropic
I = I_0 Cos[?]^2
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
F = µ0 q v I / 2pr

49. De Broglie wavelength
µ0 I / 2R
? = h/p
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
J = E s - s = Conductivity - E = Electric field

50. Angular momentum operators L^2 and L_z
? = ?0 root((1-v/c)/(1+v/c))
Cos[?] Sin[?] -Sin[?] Cos[?]
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]