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GRE Physics

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Answer 50 questions in 15 minutes.
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1. Compton Scattering
I = I_cm + md²
?? = h/mc * (1-cos(?))
Sin(?) = ?/d
µ0 I1I2 / (2pd)

2. Angular momentum operators L^2 and L_z
DW = P dV
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
µ0 I / 2pR
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>

3. EM: Series Capacitance
I = I_0 Cos[?]^2
C_eq = (? 1/C_i)^-1
N d flux / dt
.5 LI²

4. Poisson distribution (µ and s)
P +1/2 ? v² + ?gh = Constant
µ=s^2
E ~ (1/(n_f)² - 1/(n_i)²) ~ 1/?
µ0 I / 2pR

5. Energy levels from the Coulomb potential
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
T^2 = k R^3 - k=constant
L = mr²d?/dt
E_n = -µ c^2 Z a^2 / (2n^2) - with µ = m_1 m_2 / (m_1 + m_2)

6. Malus Law

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7. Hamiltonian and Hamilton'S equations
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
T = I?²/2
DW/dq
dU = 0 ? dS = ?dW/T

8. First law of thermodynamics (explain direction of energy for each term)
Exp(N(µ-e)/t)
U = t^2 d/dt (logZ)
µ=s^2
Q = U + W Q = heat in system - U = total energy in system - W = work done by gas

9. Mech: Centripetal Force
I = V/R exp(-t/RC)
F = mv²/r
? = ?_0 Sqrt[(1+v/c)/(1-v/c)]
N d flux / dt

10. Internal Energy of an Ideal Gas
(3/2) n R ?t
Measurements close to true value
L = L_0 Sqrt[1-v^2/c^2]
Const: 2t = (n +.5)? Destructive 2t = n?

11. Doppler Shift for light
?max = 2.898 x 10 -³ / T
I = Im (sinc²(a)) ; a = pai sin(?) / ?
? = ?0 root((1-v/c)/(1+v/c))
µ=s^2

12. Bohr Model: Radii
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
DW/dq
N²/Z (m_elec/m_red)
F = µ0 q v I / 2pr

13. Mech: Parallel Axis Theorem (Moment of Inertia)
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
?mv
T^2 = k R^3 - k=constant
I = I_cm + md²

14. Mech: Virial Theorem
A[B -C] = A[B -C]+[B -A]C [A -B] = -[B -A]
<T> = -<V>/2
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)
Z²/n² (m_red/m_elec)

15. Selection rules for atomic transitions
?scl = +/-1;?m = 0 - +/-1;?S_tot = 0;(?j = ?scl + ?S_tot)
A[B -C] + [A -C]B
Asin(?) = m?
Dp/dt = L / (t ?V)

16. Atom: Bohr Theory Ionization
E = Z²*E1
?= h/v(2mE)
0
N²/Z (m_elec/m_red)

17. Volumetric Expansion
DS = 0 - dQ = 0 - P V^? = constant
E = <?| H |?>
?s = 0 - ?l = ±1
V = V0 + V0 a ?T

18. QM: de Broglie Wavelength
J = ? Fdt
?= h/v(2mE)
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
P(s) = (1/Z) Exp[-E(s)/(k T)] Z = S_s(Exp[-E(s)/(k T)])

19. Quant: Orthogonality of States
1. Heat is energy 2. Entropy never decreases 3. Entropy approaches a constant value as t -> 0...
?_max = b/T
<?1|?2> = 0 ? Orthogonal
.5 LI²

20. Planck Radiation Law
Hbar*?³/(p²c³exp(hbar?/t)-1)
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
qvb = mv²/R
.5 CV²

21. EM: SHO (Hooke)
L = mr²d?/dt
L = T - V dL/dq = d/dt dL/dqdot
ma + kx = 0
DW = P dV

22. A reversible process stays..
ih_barL_z
L = mr²d?/dt
.5 CV²
Infinitely close to equilibrium at all times

23. De Broigle Wavelength
? = h/mv
1/f = (n-1)(1/R1 - 1/R2) if both positive - they are convex - concave
1/ne - where n is charge carrier density
U = t^2 d/dt (logZ)

24. Thermo: 1st Law
CdV/dt + V/R = 0 V(t) = V0 exp(-t/RC) I(t) = I(0) exp(-t/RC)
X_C = 1/(i?C)
dQ = dW +dU
Exponentially decreasing radial function

25. EM: Lorentz Force
F = qv×B
µ = m_e/2
NC?T
? = 1.22? / d

26. Bragg'S Law of Reflection
Measurements close to true value
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.
(° of Freedom)kT/2
M? = 2dsin(?)

27. Law of Mass Action
Product ( nj ^ vj ) = Product(nqj ^ vj exp (-vj F(int)/Tau))
I = -(c ?t)^2 + d^2
U = t^2 d/dt (logZ)
F = I L X B

28. Magnetic Field of a long solenoid
B = µ0 I n
F = mv²/r
V = -L di/dt
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2

29. Polarizers - intensity when crossed at ?
I = I_0 Cos[?]^2
Faraday/Lenz: current inducted opposes the changing field
B = µ0 I n
Z = ?g_i*exp(-E/kT)

30. How to derive cylcotron frequency
qvb = mv²/R
F = I L X B
I ' = I cos²(?)
<T> = -<V>/2

31. Force exerted on charge by long wire
V = V0 + V0 a ?T
F = µ0 q v I / 2pr
I = -(c ?t)^2 + d^2
Cos[?] Sin[?] -Sin[?] Cos[?]

32. Clausius-Clapeyron Equation
P1V1 - P2V2 / (? - 1)
Dp/dt = L / (t ?V)
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
SR: ?=? - ß=? E = ?mc² = v(p²c² + m²c4)

33. Single Slit Diffraction Intensity
Const: 2t = (n +.5)? Destructive 2t = n?
qvb = mv²/R
I = Im (sinc²(a)) ; a = pai sin(?) / ?
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration

34. Mech: Rotational Energy
qvb = mv²/R
H = T + V;qdot_i = dH/dp_i - pdot_i = dH/dq_i
V = V0 + V0 a ?T
T = I?²/2

35. Springs in series/parallel
P = µ_0 q^2 a^2/(6Pi c); No radiation along the axis of acceleration
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
IR + Ldi/dt = 0 - I = I0e(-tL/R) Work = 1/2 L I0^2
I = I_cm + (1/2)m d^2

36. Invariant spatial quantity
4H + 2e- ? He +2? + 6?
ds² = (c*dt)² - ?(x_i)²
Cos[?] Sin[?] -Sin[?] Cos[?]
Ct²-x²-y²-z²

37. SR: Spacetime Interval
F = R/2
<T> = -<V>/2
ds² = (c*dt)² - ?(x_i)²
I = I_0 Cos[?]^2

38. Ohm'S Law w/ current density
J = E s - s = Conductivity - E = Electric field
Opposing charge induced upon conductor
µ=s^2
I_z = I_x + I_y (think hoop symmetry)

39. Delta Function Potential - type of WF
J = E s - s = Conductivity - E = Electric field
? = h/mv
<T> = -<V>/2
Exponential - E = -ma²/2hbar² - a is strength of delta wellt

40. Wein'S displacement law for blackbodies (? and T)
dQ = dW +dU
Hbar*?³/(p²c³exp(hbar?/t)-1)
U - ts = -tlog(Z)
?_max = b/T

41. Energy for orbits: Hyperbole - Ellipse - Parabola - Circle
µ0 I / 2R
D/dt (.5*r^2 d?/dt) = 0 - r(?) = a(1-e²)/(1+ecos(?)) - T²aA³
E = Vmin : circle - E = 0 : parabola - E<0 : el - E>0 : h
PdV +dU

42. EM: Electric Field inside of Conductor
? (t-vx/c²)
0
Series: 1/k_eq = 1/k_1 + 1/k_2; Parallel: k_eq = k_1 + k_2
P² ~ R³

43. Single Slit Diffraction Maximum
Asin(?) = m?
L^2 |E - scl - m> = hbar^2 scl(scl+1) |E -scl -m> L_z |E - scl - m> = hbar m |E - scl - m>
? = 1.22? / d
?~T

44. Double Slit: Interference Minimum - Diffraction Minimum
F = qv×B
F = f* (c+v_r)/(c+v_s)
Dv = -udm/m - v = v0 + u ln(m0/m)
Interference: (m+.5)? = d sin(?) Diffraction: m? = w sin(?)

45. Rocket Equation
T^2 = k R^3 - k=constant
C_eq = (? 1/C_i)^-1
I_z = I_x + I_y (think hoop symmetry)
Dv = -udm/m - v = v0 + u ln(m0/m)

46. Perpendicular axis theorem
?mc²
<?|O|?>
I_z = I_x + I_y (think hoop symmetry)
F = s * T4

47. Force/length between two wires
dU = 0 ? dS = ?dW/T
.5 CV²
µ0 I1I2 / (2pd)
I = I_cm + (1/2)m d^2

48. Energy in terms of partition function
U = t^2 d/dt (logZ)
<?1|?2> = 0 ? Orthogonal
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
N²/Z (m_elec/m_red)

49. Mech: Impulse
Let w_i = 1/s_i^2;x_wav = S(w_i x_i) / Sw_i - s_xwav = 1/Sw_i
Const: 2t = (n +.5)? Destructive 2t = n?
J = ? Fdt
µ = m_e/2

50. Relativistic length contraction
Dv = -udm/m - v = v0 + u ln(m0/m)
?L/A - L = length - A = cross sectional area - rho is electrical resistivity
L = µ N² A / l : N = number of turns - A = cross sectional area -l = length
L = L_0 Sqrt[1-v^2/c^2]

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