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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. Polarizers - intensity when crossed at ?
<?|O|?>
I = I_0 Cos[?]^2
(3/2) n R ?t
J = E s - s = Conductivity - E = Electric field

2. Invariant Energy Quantity
E²-p²c²
L = mr²d?/dt
Const: 2t = (n +.5)? Destructive 2t = n?
Dp/dt = L / (t ?V)

3. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
? (t-vx/c²)
µ0 I1I2 / (2pd)
dQ = dW +dU

4. Bohr Model: Radii
Q = CVexp(-t/RC)
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
N²/Z (m_elec/m_red)

5. Relativistic Energy
Z_c = -i/(?C) ; Z_L = i ? L
L = T - V dL/dq = d/dt dL/dqdot
F = -2*m(? x r)
?mc²

6. Perpendicular axis theorem
? = h/mv
F = f* (c+v_r)/(c+v_s)
I_z = I_x + I_y (think hoop symmetry)
µ = Current * Area T = µ x B

7. Boltzmann / Canonical distribution
µ = m_e/2
Z²/n² (m_red/m_elec)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])
? = h/mv

8. Thermo: 1st Law
dQ = dW +dU
? = ?0 root((1-v/c)/(1+v/c))
E = s/e_0
F = f* (c+v_r)/(c+v_s)

9. Energy levels from the Coulomb potential
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
µ = m_e/2
L = L_0 Sqrt[1-v^2/c^2]
Measurements close to mean

10. De Broglie wavelength
C_eq = ?C_i
Ct²-x²-y²-z²
? = h/p
T = I?²/2

11. Work (P - V)
Infinitely close to equilibrium at all times
J/(ne) n: atom density
P1V1 - P2V2 / (? - 1)
? = h/mv

12. Selection rules for atomic transitions
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
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.
v(mean)

13. Quant: Commutator Relation [AB -C]
A[B -C] + [A -C]B
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
v(mean)
qvb = mv²/R

14. Compton Scattering
F = qv×B
?? = h/mc * (1-cos(?))
<T> = 1/2 * <dV/dx>
P1V1 - P2V2 / (? - 1)

15. Kepler'S third law (T and R)
Cv = dE/dT = 3R
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
C_eq = ?C_i
T^2 = k R^3 - k=constant

16. Quant: Orthogonality of States
X_C = 1/(i?C)
<?1|?2> = 0 ? Orthogonal
T^2 = k R^3 - k=constant
?_max = b/T

17. Energy in Inductor
N d flux / dt
.5 LI²
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
?= h/v(2mE)

18. Lab: Precision of Measurements
I = I_0 Cos[?]^2
Dv = -udm/m - v = v0 + u ln(m0/m)
Measurements close to mean
P/A = s T^4

19. Addition of relativistic velocities

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20. Magnetic field due to a segment of wire
?max = 2.898 x 10 -³ / T
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
F = s * T4
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)

21. First law of thermodynamics (explain direction of energy for each term)
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
Q = CVexp(-t/RC)
ih_barL_z
µ = m_e/2

22. Delta Function Potential - type of WF
? = 1.22? / d
Always Real
? (t-vx/c²)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

23. Springs in series/parallel
P1V1 - P2V2 / (? - 1)
µ = Current * Area T = µ x B
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Z_C + Z_L = 0. Occurs when ?=1/Sqrt[L C]

24. Relativistic length contraction
ds² = (c*dt)² - ?(x_i)²
L = L_0 Sqrt[1-v^2/c^2]
F = qv×B
F = s * T4

25. Rocket Thrust
S = k ln[O] ; dS = dQ/T
Opposing charge induced upon conductor
I = I_cm + md²
u dm/dt

26. Expectation value of the energy of state |?>
E = <?| H |?>
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
0
?~T

27. E field of a capacitor (d->0)
I_z = I_x + I_y (think hoop symmetry)
U - ts = -tlog(Z)
E = s/e_0
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

28. Clausius-Clapeyron Equation
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
Dp/dt = L / (t ?V)
T = I?²/2
E = <?| H |?>

29. Rocket Equation
V = V0 + V0 a ?T
Z = ?g_i*exp(-E/kT)
Dv = -udm/m - v = v0 + u ln(m0/m)
F = qv×B

30. Induced EMF of solenoid
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 ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
N d flux / dt
?mc²

31. How to derive cylcotron frequency
J = ? Fdt
? exp(-e/t)
µ0 I1I2 / (2pd)
qvb = mv²/R

32. Mech: Virial Theorem
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.
<T> = 1/2 * <dV/dx>
?mv
<T> = -<V>/2

33. Pauli matrices
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
P² ~ R³
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
E²-p²c²

34. EM: Method of Images
0
Opposing charge induced upon conductor
I = V/R exp(-t/RC)
µ0 I1I2 / (2pd)

35. Mech: Impulse
F = f* (c+v_r)/(c+v_s)
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
ih_barL_z
J = ? Fdt

36. EM: Electric Field inside of Conductor
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
0
F = R/2
? = 5/3

37. SR: Total Energy of a Particle
ds² = (c*dt)² - ?(x_i)²
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
0
Faraday/Lenz: current inducted opposes the changing field

38. Single Slit Diffraction Maximum
? = 5/3
dQ = dW +dU
Asin(?) = m?
J = E s - s = Conductivity - E = Electric field

39. Stefan-Boltzmann law for blackbodies (power per area and T)
P/A = s T^4
?mv
Hbar*?³/(p²c³exp(hbar?/t)-1)
T^2 = k R^3 - k=constant

40. Helmholtz Free Energy
KE = 1/2 * µ (dr/dt)² L = µ r x v
0
P +1/2 ? v² + ?gh = Constant
U - ts = -tlog(Z)

41. Commutator identities ( [B -A C] - [A -B] )
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
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
I = I_0 Cos[?]^2
I = I_cm + (1/2)m d^2

42. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
Const: 2t = (n +.5)? Destructive 2t = n?
µ = Current * Area T = µ x B
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

43. Doppler Shift for light
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
? = 5/3
? = ?0 root((1-v/c)/(1+v/c))

44. EM: Maxwell'S equations
<T> = -<V>/2
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)
qvb = mv²/R
F = R/2

45. Complex impedance (expressions for capacitor and inductor)
I = V/R exp(-t/RC)
Z²/n² (m_red/m_elec)
Z_c = -i/(?C) ; Z_L = i ? L
µ = m_e/2

46. Self Inductance
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Opposing charge induced upon conductor
V = -L di/dt
Isentropic

47. Anomalous Zeeman Effect

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48. Partition Function
Q = CVexp(-t/RC)
Int ( A . dr) = Int ( del x A) dSurface
V = -L di/dt
? exp(-e/t)

49. Bohr Model: Energy
J = ? Fdt
? (t-vx/c²)
Z²/n² (m_red/m_elec)
0

50. Atom: Positronium Reduced Mass
1/vLC
Cos[?] Sin[?] -Sin[?] Cos[?]
µ = m_e/2
1/ne - where n is charge carrier density