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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: Expectation Value
Hbar*?³/(p²c³exp(hbar?/t)-1)
DW/dq
<?|O|?>
dU = 0 ? dS = ?dW/T

2. Stefan-Boltzmann law for blackbodies (power per area and T)
X_C = 1/(i?C)
P1V1 - P2V2 / (? - 1)
P/A = s T^4
? = h/p

3. De Broigle Wavelength
J = ? Fdt
<?1|?2> = 0 ? Orthogonal
? = h/mv
qvb = mv²/R

4. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
E²-p²c²
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
4H + 2e- ? He +2? + 6?

5. Work done on a gas
I ' = I cos²(?)
dQ = dW +dU
F = qv×B
DW = P dV

6. Bar magnets -- direction of B field lines - earth'S B field
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
I = Im (sinc²(a)) ; a = pai sin(?) / ?
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

7. Helmholtz Free Energy
I ' = I cos²(?)
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
U - ts = -tlog(Z)
W_A < W_I

8. Mech: Rotational Energy
ds² = (c*dt)² - ?(x_i)²
T = I?²/2
S_mean = s/Sqrt[N]
1/vLC

9. Kepler'S Three Laws
u dm/dt
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
I = I_0 Cos[?]^2
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³

10. 3 Laws of Thermo
KE = 1/2 * µ (dr/dt)² L = µ r x v
C_eq = ?C_i
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

11. Relativistic Energy
Opposing charge induced upon conductor
?mc²
ih_barL_z
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i

12. Malus Law

13. Adiabatic processes (dS - dQ - P and V)
ma + kx = 0
I = V/R exp(-t/RC)
.5 LI²
DS = 0 - dQ = 0 - P V^? = constant

14. Perturbations
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
dU = 0 ? dS = ?dW/T
H = H_0 + ?H
I = I_cm + (1/2)m d^2

15. Rocket Thrust
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
u dm/dt
I_z = I_x + I_y (think hoop symmetry)

16. EM: Bremsstrahlung (translation)
Braking Radiation
?_max = b/T
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

17. Expectation value of the energy of state |?>
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
(3/2) n R ?t
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
E = <?| H |?>

18. Commutator identities ( [B -A C] - [A -B] )
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
?mc²
H = H_0 + ?H
F = µ0 q v I / 2pr

19. EM: Reactance of Inductor
X_L = i?L
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
W_A < W_I

20. Magnetic Field For Current in Long Wire
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
µ0 I / 2pR
W_A < W_I

21. Triplet/singlet states: symmetry and net spin
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
J = ? Fdt
? = 1.22? / d
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2

22. Self Inductance
A[B -C] + [A -C]B
V = -L di/dt
Asin(?) = m?
DW = P dV

23. Hall Coefficient
1/ne - where n is charge carrier density
Measurements close to true value
Exponential - E = -ma²/2hbar² - a is strength of delta wellt
<?1|?2> = 0 ? Orthogonal

24. Energy in terms of partition function
U = t^2 d/dt (logZ)
P +1/2 ? v² + ?gh = Constant
u dm/dt
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

25. Thermo: 1st Law
.5 LI²
dQ = dW +dU
F = µ0 q v I / 2pr
Faraday/Lenz: current inducted opposes the changing field

26. Angular momentum operators L^2 and L_z
Q = CVexp(-t/RC)
Infinitely close to equilibrium at all times
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
E²-p²c²

27. EM: Method of Images
C_eq = ?C_i
Opposing charge induced upon conductor
ih_barL_z
? = h/mv

28. De Broglie wavelength
4H + 2e- ? He +2? + 6?
I = I_cm + md²
L = mr²d?/dt
? = h/p

29. Force exerted on charge by long wire
ma + kx = 0
?_max = b/T
F = µ0 q v I / 2pr
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?

30. Pauli matrices
C_eq = ?C_i
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
1s² - 2s² 2p6 - 3s² 3p6 3d¹°
KE = 1/2 * µ (dr/dt)² L = µ r x v

31. Atom: Orbital Config
Q = CVexp(-t/RC)
F = s * T4
V = V0 + V0 a ?T
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

32. Rotation matrix (2x2)
Cos[?] Sin[?] -Sin[?] Cos[?]
?= h/v(2mE)
?_max = b/T
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.

33. Effective Potential
V(r) + L²2/2mr²
<?1|?2> = 0 ? Orthogonal
KE = 1/2 * µ (dr/dt)² L = µ r x v
N d flux / dt

34. EM: AC Resonance
Braking Radiation
X_L = X_C or X_total = 0
µ=s^2
? exp(-e/t)

35. Hamiltonian and Hamilton'S equations
Always Real
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
I = Im (sinc²(a)) ; a = pai sin(?) / ?
NC?T

36. Magnetic Field of a long solenoid
B = µ0 I n
Asin(?) = m?
I = Im (sinc²(a)) ; a = pai sin(?) / ?
F = I L X B

37. Thin Film Theory: Constructive / Destructive Interference
u dm/dt
?_max = b/T
X_C = 1/(i?C)
Const: 2t = (n +.5)? Destructive 2t = n?

38. Adiabatic means
Dp/dt = L / (t ?V)
Isentropic
Measurements close to true value
Dv = -udm/m - v = v0 + u ln(m0/m)

39. Wein'S displacement law for blackbodies (? and T)
V(r) + L²2/2mr²
N d flux / dt
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
?_max = b/T

40. Thermo: Blackbody Radiation
F = s * T4
F = I L X B
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

41. Quant: Commutator Relation [AB -C]
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
F = R/2
A[B -C] + [A -C]B

42. Boltzmann / Canonical distribution
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
NC?T
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
L = mr²d?/dt

43. Focal point of mirrror with curvature
F = -2*m(? x r)
?mv
J = E s - s = Conductivity - E = Electric field
F = R/2

44. Stark Effect
F = -2*m(? x r)
? = 5/3
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
<?|O|?>

45. td(entropy) =
u dm/dt
F = mv²/r
E = s/e_0
PdV +dU

46. Bragg'S Law of Reflection
M? = 2dsin(?)
?mv
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
L = L_0 Sqrt[1-v^2/c^2]

47. Work (P - V)
?= h/v(2mE)
Braking Radiation
P1V1 - P2V2 / (? - 1)
µ = m_e/2

48. Magnetic Field Through Ring
µ0 I / 2R
M? = 2dsin(?)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
0

49. Planck Radiation Law
N²/Z (m_elec/m_red)
L = mr²d?/dt
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
Hbar*?³/(p²c³exp(hbar?/t)-1)

50. Mech: Virial Theorem
F = I L X B
Cos[?] Sin[?] -Sin[?] Cos[?]
dQ = dW +dU
<T> = -<V>/2