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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. Invariant Energy Quantity
M? = 2dsin(?)
E²-p²c²
Dp/dt = L / (t ?V)
1s² - 2s² 2p6 - 3s² 3p6 3d¹°

2. Triplet/singlet states: symmetry and net spin
P +1/2 ? v² + ?gh = Constant
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0
North to south; Earth has S magnetic pole at the N geographic pole and vice versa.
Dv = -udm/m - v = v0 + u ln(m0/m)

3. How to derive cylcotron frequency
Isentropic
I = -(c ?t)^2 + d^2
qvb = mv²/R
? exp(-e/t)

4. Single Slit Diffraction Maximum
E²-p²c²
Asin(?) = m?
?max = 2.898 x 10 -³ / T
X_L = X_C or X_total = 0

5. Quant: Eigenvalue of Hermitian Operator
Ct²-x²-y²-z²
I = I_0 Cos[?]^2
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Always Real

6. Lab: Precision of Measurements
?max = 2.898 x 10 -³ / T
Measurements close to mean
dQ = dW +dU
.5 LI²

7. De Broglie wavelength
? = h/p
Cos[?] Sin[?] -Sin[?] Cos[?]
J = ? Fdt
V = V0 + V0 a ?T

8. Relativistic interval (which must remain constant for two events)
1/2 CV²
I = -(c ?t)^2 + d^2
1/ne - where n is charge carrier density
F_f = µ*F_N

9. Resistance - length - area - rho
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity

10. Time Lorentz Transformation
C_eq = (? 1/C_i)^-1
?_max = b/T
? (t-vx/c²)
S_mean = s/Sqrt[N]

11. Polarizers - intensity when crossed at ?
I = I_0 Cos[?]^2
L = T - V dL/dq = d/dt dL/dqdot
X_C = 1/(i?C)
P1V1 - P2V2 / (? - 1)

12. Mech: Parallel Axis Theorem (Moment of Inertia)
DW = P dV
F_f = µ*F_N
I = I_cm + md²
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

13. Mean electron drift speed
(° of Freedom)kT/2
Q = CVexp(-t/RC)
J/(ne) n: atom density
Triplet: symmetric - net spin 1 Singlet: antisymmetric - net spin 0

14. Force exerted on charge by long wire
F = µ0 q v I / 2pr
Z_c = -i/(?C) ; Z_L = i ? L
0
Cv = dE/dT = 3R

15. 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
? = 1.22? / d
? = h/p
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

16. SR: Total Energy of a Particle
F = µ0 q v I / 2pr
0
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

17. Magnetic Dipole Moment and Torque
F_f = µ*F_N
µ = Current * Area T = µ x B
(° of Freedom)kT/2
S = k ln[O] ; dS = dQ/T

18. Energy in terms of partition function
ih_barL_z
<T> = 1/2 * <dV/dx>
U = t^2 d/dt (logZ)
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

19. Adiabatic processes (dS - dQ - P and V)
.5 CV²
DS = 0 - dQ = 0 - P V^? = constant
? (t-vx/c²)
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.

20. Work (P - V)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
KE = 1/2 * µ (dr/dt)² L = µ r x v
P1V1 - P2V2 / (? - 1)
I = -(c ?t)^2 + d^2

21. Anomalous Zeeman Effect

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22. Center of Mass: Kinetic Energy & Angular Momentum
KE = 1/2 * µ (dr/dt)² L = µ r x v
ma + kx = 0
(° of Freedom)kT/2
µ = m_e/2

23. Force/length between two wires
<T> = -<V>/2
?~T
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.
µ0 I1I2 / (2pd)

24. Commutator identities ( [B -A C] - [A -B] )
Isentropic
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
N d flux / dt
T^2 = k R^3 - k=constant

25. Atom: Bohr Theory Ionization
(3/2) n R ?t
Sin(?) = ?/d
µ = Current * Area T = µ x B
E = Z²*E1

26. Source-free RC Circuit
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
µ0 I / 2R
Asin(?) = m?

27. Ohm'S Law w/ current density
J = E s - s = Conductivity - E = Electric field
Int ( A . dr) = Int ( del x A) dSurface
E²-p²c²
Cos[?] Sin[?] -Sin[?] Cos[?]

28. First law of thermodynamics (explain direction of energy for each term)
Cv = dE/dT = 3R
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...

29. Complex impedance (expressions for capacitor and inductor)
Z_c = -i/(?C) ; Z_L = i ? L
ma + kx = 0
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
v(mean)

30. EM: SHO (Hooke)
ma + kx = 0
?max = 2.898 x 10 -³ / T
F = I L X B
I = I_cm + (1/2)m d^2

31. Magnetic Field of a long solenoid
B = µ0 I n
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
I = I_cm + md²
Measurements close to mean

32. Quant: Commutator Relation [AB -C]
F = f* (c+v_r)/(c+v_s)
A[B -C] + [A -C]B
4H + 2e- ? He +2? + 6?
div(E) = ?/e_0 - curl(E) = der(B)/der(t) - div(B) = 0 - curl(B) = µ_0J + µ_0e_0*der(E)/der(t)

33. Law of Mass Action
? = 5/3
DB = ( µ_0 I/(4Pi) ) dl(cross)rhat/r^2
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
Z²/n² (m_red/m_elec)

34. Delta Function Potential - type of WF
Ct²-x²-y²-z²
I = I_cm + (1/2)m d^2
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.
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

35. Mech: Impulse
S = k ln[O] ; dS = dQ/T
4H + 2e- ? He +2? + 6?
J = ? Fdt
L = L_0 Sqrt[1-v^2/c^2]

36. Magnetic Field For Current in Long Wire
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
µ0 I1I2 / (2pd)
µ0 I / 2pR

37. Lab: Standard Deviation of Poisson
v(mean)
?s = 0 - ?l = ±1
Sin(?) = ?/d
I = Im (sinc²(a)) ; a = pai sin(?) / ?

38. Selection rules for atomic transitions
B = µ0 I (sin(?1)-sin(?2))/(4pr) r = distance from point
Exponentially decreasing radial function
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
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)

39. Springs in series/parallel
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
Isentropic
µ0 I / 2pR
?~1/T

40. SR: Spacetime Interval
ds² = (c*dt)² - ?(x_i)²
0
dQ = dW +dU
µ0 I1I2 / (2pd)

41. Stefan-Boltzmann law for blackbodies (power per area and T)
X_L = i?L
Ct²-x²-y²-z²
P/A = s T^4
I = Im (sinc²(a)) ; a = pai sin(?) / ?

42. td(entropy) =
X_L = i?L
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
H = H_0 + ?H
PdV +dU

43. Thermo: Blackbody Radiation
Isentropic
F = s * T4
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)
qvb = mv²/R

44. Planck Radiation Law
?= h/v(2mE)
PdV +dU
Cv = dE/dT = 3R
Hbar*?³/(p²c³exp(hbar?/t)-1)

45. Rotation matrix (2x2)
Cos[?] Sin[?] -Sin[?] Cos[?]
? exp(-e/t)
<T> = -<V>/2
J = ? Fdt

46. QM: de Broglie Wavelength
N²/Z (m_elec/m_red)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)
?= h/v(2mE)
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

47. De Broigle Wavelength
? = h/mv
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas
ih_barL_z
L = T - V dL/dq = d/dt dL/dqdot

48. EM: Reactance of Inductor
DW/dq
E = s/e_0
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
X_L = i?L

49. Energy in a Capacitor
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.
I_z = I_x + I_y (think hoop symmetry)
.5 CV²
F_f = µ*F_N

50. Rayleigh criterion
µ=s^2
<T> = -<V>/2
? = 1.22? / d
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.