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Hill Amster

Hill A.

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Viewed Questions

Use Equation $6.59$ to estimate the internal field in hydrogen, and characterize quantitatively a "strong" and "weak" Zeeman field.

Use Equation $6.59$ to estimate the internal field in hydrogen, and characterize quantitatively a "strong" and "weak" Zeeman field.

Introduction to Quantum Mechanics

Time-independent Perturbation Theory

The Zeeman Effect

Let $G=\langle A, B\rangle \leq \mathrm{GL}(2, \mathrm{C})$, where $$A=\left[\begin{array}{ll}0 & i \\i & 0\end{array}\right] \quad \text { and } \quad B=\left[\begin{array}{rr}0 & 1 \\ -1 & 0\end{array}\right]$$ Show that $G$ is a nonabelian group (so $G$ is not cyclic) of order 8 having a unique subgroup of order 2. (See Theorem 4.22.)

An Introduction to the Theory of Groups

Use the eigenfunction of Problem 24 to calculate the following expectation values, and comment on each result: (a) $\bar{x}$, (b) $\bar{p}$, (c) $\overline{x^{2}}$, (d) $p^{2}$

Use the eigenfunction of Problem 24 to calculate the following expectation values, and comment on each result: (a) $\bar{x}$, (b) $\bar{p}$, (c) $\overline{x^{2}}$, (d) $p^{2}$

Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles

Solutions Of Time-Independent…

Problems
Consider a Kerr cell whose plates are separated by a distance $d$ Let $\ell$ be the effective length of those plates (slightly different from the actual length because of fringing of the field). Show that $$\Delta \varphi=2 \pi K \ell V^{2} / d^{2}$$

Consider a Kerr cell whose plates are separated by a distance $d$ Let $\ell$ be the effective length of those plates (slightly different from the actual length because of fringing of the field). Show that $$\Delta \varphi=2 \pi K \ell V^{2} / d^{2}$$

Optics

Questions asked

INSTANT ANSWER

The supersonic two-dimensional intake shown in Figure has three oblique shocks and a final normal shock. The first wedge angle is δ=5°. Each subsequent wedge has an additional 1°. The flight Mach number is 2.2. What will be the efficiency of the intake? For a flight altitude of 9 km, calculate the static and total pressures downstream each shock.

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INSTANT ANSWER

The fighter aircraft (F-111A) described in Example 9.6 has an automatic inlet control system. This system senses the local Mach number and then moves the spike longitudinally. If the spike deflection angle is constant (δ=12.5°), calculate the distance (x) for spike at flight Mach number M=1.9, M=2.2, and M=2.5

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INSTANT ANSWER

During cruise flight, the ambient conditions and the intake conditions in a turbofan engine are P∞=23.824 kPa, T∞=218.665 K, total air mass flow rate of engine m=118 kg/s. Mach numbers are as follows: Far upstream: M∞=0.85, at diffuser inlet (capture section) Mc=0.8 and fan inlet Mf=0.50. Assuming the diffuser pressure recovery: d=095. a) Determine the diameters at far upstream (d), intake inlet section (dc), and intake outlet section (or fan inlet section: df). Assume the hub-tip ratio of fan is 0.3. b) Diffuser length L (assume that the diffuser angle 2θ is 12°)

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ANSWERED

Penny Riley verified

Numerade educator

A? A_c A_t ?_1 ?_2

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INSTANT ANSWER

The figure shown illustrates a supersonic intake of an engine installed on the lower surface of the wing of a fighter airplane. The airplane has a maximum Mach number of 2.3. Two shocks are generated (oblique and normal) and the long duct upstream of the engine is a subsonic part having a pressure drop of 10%. The Mach number at the engine inlet is 0.5, which is 15% less than the Mach number downstream of the normal shock wave. a) Calculate the wedge angle of the oblique shock wave. b) What will be the overall pressure ratio of this intake? c) Have you any suggestions?

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INSTANT ANSWER

The two-dimensional or wedge-type diffuser consists of two external oblique shocks: a normal shock and a subsonic diffuser, as shown in the following figure. Assuming that the external losses are due to the shock losses and the pressure drop in the subsonic part is 4.5%, 1. Determine the total pressure ratio for the shown Mach number of 3.5. 2. What will be the external length of the wedge if the height of intake is 0.5 m?

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INSTANT ANSWER

9.3 A supersonic fighter has the shown intake that is fitted with a movable spike. The circular intake has an inlet radius \( R=1 \mathrm{~m} \). During ground run, the following data was recorded: \begin{tabular}{cc} Air mass flow rate & \( 350 \mathrm{~kg} / \mathrm{s} \) \\ \hline Ambient temperature & \( 288 \mathrm{~K} \) \\ \hline Ambient pressure & \( 101 \mathrm{kPa} \) \\ \hline Free stream velocity & \( 100 \mathrm{~m} / \mathrm{s} \) \end{tabular} What will be the distance \( x \) of the outer portion of the spike? FIGURE P9.3 If the needed mass flow rate becomes \( 380 \mathrm{~m} / \mathrm{s} \), two options are suggested: either retracting the spike to increase the inlet area or opening the 8 blow-up doors. Calculate the new position of the spike \( \left(x^{\prime}\right) \). If the blow-up doors are opened, calculate the length of the doors, if the subtended angle to each door is \( 30^{\circ} \) and the length \( L \) is equal to \( 1.6 \mathrm{~m} \).

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ANSWERED

Anand Jangid verified

Numerade educator

Two objects A and B are connected by a thin string and are at rest on a smooth plane. The mass of A is 3 kg, and the mass of B is 2 kg. A constant force is now applied to B, resulting in an impulse of 20 N·s. If the string suddenly breaks during the application of the force, and eventually vA = 3 m/s, then vB = [ ] m/s. If the duration from the start of the force application to the breaking of the string is 10 seconds, then the force F = [ ] N. A ---- B -> F

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ANSWERED

T. L. verified

Numerade educator

求曲線x^2=2y及y-x=4所圍的區域面積

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ANSWERED

Taha T verified

Numerade educator

2x^2y +z^3 =5xy^2 +yz, (1) ∂z/∂x=? (2) ∂z/∂y=?

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