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GRE Physics

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Quant: Eigenvalue of Hermitian Operator
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
Always Real
<T> = 1/2 * <dV/dx>
I_z = I_x + I_y (think hoop symmetry)

2. Spherical Capacitor Equation
NC?T
ma + kx = 0
I = I_0 Cos[?]^2
C = 4pe0 ab/(a-b) = inner and outer radii

3. Wein'S Displacement Law
?max = 2.898 x 10 -³ / T
µ = m_e/2
V = -L di/dt
? = h/p

4. Doppler shift for light
V = V0 + V0 a ?T
I = Im (sinc²(a)) ; a = pai sin(?) / ?
F = f* (c+v_r)/(c+v_s)
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]

5. Rotation matrix (2x2)
L = L_0 Sqrt[1-v^2/c^2]
E = <?| H |?>
Cos[?] Sin[?] -Sin[?] Cos[?]
L = mr²d?/dt

6. Bragg'S Law of Reflection
N²/Z (m_elec/m_red)
M? = 2dsin(?)
A[B -C] + [A -C]B
v(mean)

7. Law of Mass Action
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
X_L = X_C or X_total = 0
? exp(-e/t)

8. EM: Bremsstrahlung (translation)
?mv
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
<T> = -<V>/2
Braking Radiation

9. Atom: Positronium Reduced Mass
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
4H + 2e- ? He +2? + 6?
µ = m_e/2
V(r) + L²2/2mr²

10. Work (P - V)
P1V1 - P2V2 / (? - 1)
Measurements close to true value
F = s * T4
?~1/T

11. Thermo: 1st Law
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
A[B -C] + [A -C]B
dQ = dW +dU
Z_c = -i/(?C) ; Z_L = i ? L

12. Boltzmann / Canonical distribution
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
Sin(?) = ?/d
(° of Freedom)kT/2
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

13. Perturbations
0
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
u dm/dt
H = H_0 + ?H

14. Rocket Equation
Dv = -udm/m - v = v0 + u ln(m0/m)
Cos[?] Sin[?] -Sin[?] Cos[?]
P1V1 - P2V2 / (? - 1)
J = ? Fdt

15. Solid: Resistivity of Metal
Z²/n² (m_red/m_elec)
F = mv²/r
Q = CVexp(-t/RC)
?~T

16. EM: Maxwell'S equations
F = s * T4
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
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[?]

17. Quant: [L_x -L_y] = ?
ih_barL_z
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
µ = Current * Area T = µ x B
P/A = s T^4

18. Mech: Force of Friction
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
X_L = i?L
E = <?| H |?>
F_f = µ*F_N

19. Force on a wire in magnetic field
E = <?| H |?>
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
F = I L X B
V(r) + L²2/2mr²

20. Force exerted on charge by long wire
<?|O|?>
F = µ0 q v I / 2pr
KE = 1/2 * µ (dr/dt)² L = µ r x v
I = I_0 Cos[?]^2

21. Planck Radiation Law
P1V1 - P2V2 / (? - 1)
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
Hbar*?³/(p²c³exp(hbar?/t)-1)
Dv = -udm/m - v = v0 + u ln(m0/m)

22. Poisson distribution (µ and s)
µ0 I / 2pR
?= h/v(2mE)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
µ=s^2

23. Commutator identities ( [B -A C] - [A -B] )
1/2 CV²
F = s * T4
?~1/T
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]

24. EM: Electric Field inside of Conductor
Q = CVexp(-t/RC)
E = s/e_0
0
F = -2*m(? x r)

25. Addition of relativistic velocities

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26. Source Free RL Circuit
L = mr²d?/dt
F = mv²/r
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
V(r) + L²2/2mr²

27. Malus Law

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28. Kepler'S Three Laws
I = V/R exp(-t/RC)
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
Z²/n² (m_red/m_elec)
L = L_0 Sqrt[1-v^2/c^2]

29. Mech: Impulse
J = ? Fdt
E = <?| H |?>
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
Cv = dE/dT = 3R

30. De Broigle Wavelength
KE = 1/2 * µ (dr/dt)² L = µ r x v
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
dU = 0 ? dS = ?dW/T
? = h/mv

31. Triplet/singlet states: symmetry and net spin
<?|O|?>
L = L_0 Sqrt[1-v^2/c^2]
J = E s - s = Conductivity - E = Electric field
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

32. Rayleigh'S Criterion
Z_c = -i/(?C) ; Z_L = i ? L
X_L = i?L
Sin(?) = ?/d
S = k ln[O] ; dS = dQ/T

33. Thermo: Blackbody Radiation
<?|O|?>
F = s * T4
µ = m_e/2
Q = CVexp(-t/RC)

34. Wein'S displacement law for blackbodies (? and T)
F = qv×B
(° of Freedom)kT/2
Isentropic
?_max = b/T

35. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
I = V/R exp(-t/RC)
X_L = i?L
<T> = -<V>/2

36. EM: Electromagnetic inertia
Faraday/Lenz: current inducted opposes the changing field
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.
?~1/T
?_max = b/T

37. Lensmaker Equation - Thin Lens
I = I_cm + (1/2)m d^2
Z = ?g_i*exp(-E/kT)
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
C = 4pe0 ab/(a-b) = inner and outer radii

38. EM: Series Capacitance
C_eq = (? 1/C_i)^-1
I = I_cm + md²
J/(ne) n: atom density
1/vLC

39. Adiabatic means
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
Int ( A . dr) = Int ( del x A) dSurface
Isentropic

40. Atom: Bohr Theory Ionization
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
F = I L X B
F = R/2
E = Z²*E1

41. Clausius-Clapeyron Equation
Dp/dt = L / (t ?V)
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
1/vLC
Exponentially decreasing radial function

42. Compton Scattering
W_A < W_I
?s = 0 - ?l = ±1
I = V/R exp(-t/RC)
?? = h/mc * (1-cos(?))

43. Bernoulli Equation
P +1/2 ? v² + ?gh = Constant
?_max = b/T
F = I L X B
PdV +dU

44. Bohr Model: Energy
4H + 2e- ? He +2? + 6?
Z²/n² (m_red/m_elec)
L = T - V dL/dq = d/dt dL/dqdot
µ0 I / 2R

45. Bohr Model: Radii
L = T - V dL/dq = d/dt dL/dqdot
(° of Freedom)kT/2
P² ~ R³
N²/Z (m_elec/m_red)

46. QM: de Broglie Wavelength
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
?= h/v(2mE)
? (t-vx/c²)
Dp/dt = L / (t ?V)

47. Bar magnets -- direction of B field lines - earth'S B field
X_L = X_C or X_total = 0
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Sin(?) = ?/d

48. Focal point of mirrror with curvature
P +1/2 ? v² + ?gh = Constant
F_f = µ*F_N
F = R/2
Sin(?) = ?/d

49. RLC resonance condition
(3/2) n R ?t
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
Z²/n² (m_red/m_elec)
1/vLC

50. Error in the mean if each measurement has the same uncertainty s
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
Const: 2t = (n +.5)? Destructive 2t = n?
S_mean = s/Sqrt[N]
DS = 0 - dQ = 0 - P V^? = constant