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Spherical tensor operators Given: Az = ¿ bemPem(s) (1) m =-l Where Tem are the tesseral...
6Show that the Eulerian strain rate is given by 147 and [see Eq. (3.5.10) for the definition of al e D. 3.5.3 Infinitesimal Rotation Tensor The displacement gradient tensor can be expressed as the sum of tensor and a skew symmetric tensor. We have of a symmetric where the symmetric part is similar to the infinitesimal strain tensor (and when l▽u| ~ |▽oul << 1), and the skew symmetric part is known as the infinitesimal rotation tensor lelilt lh the...
A spin-1 particle interacts with an external magnetic field B = B. The interaction Hamiltonian for the system is H = gB-S, where S-Si + Sỳ + SE is the spin operator. (Ignore all degrees of freedom other than spin.) (a) Find the spin matrices in the basis of the S. S eigenstates, |s, m)) . (Hint: Use the ladder operators, S -S, iS, and S_-S-iS,, and show first that s_ | 1,0-ћ /2 | 1.-1)) . Then use these...
4. 10 points The Spin operators for a spin-1/2 particle can be described by the Pauli matrices: 0 1 0 0 ,02= 0 -1 1 ¿ a) Write the normalized eigenvectors of Oz, I+) and 1-) which are defined such that 0z|+) = 1+) and 0z1-) = -1-), as column vectors in the same basis as the Pauli matrices given above. (You can assume without loss of generality that these eigenvectors are real.) (3 pts) b) Consider an eigenvector (V)...
Exercise 17.3.4.* We discuss here some tricks for evaluating the expectation values of certain operators in the eigenstates of hydrogen. (1) Suppose we want (1/ r m. Consider first (2/r). We can interpret ( r) as the first- order correction due to a perturbation 1/r. Now this problem can be solved exactly; we just replace e? by e- 2 everywhere. (Why?) So the exact energy, from Eq. (13.1.16) is E(X) = -(e-2) m/2n'h. The first-order correction is the term linear...
2. A version of the "IS-LM macroeconomic model leads to the system of equations: 1. 1 (r) = S(Y) 2.aY + L(r) = M where a is a parameter, and I,S, and L are given differentiable functions. Suppose that the system defines Y and r implicitly as differentiable function of a and M. find ov and ar ам
2. A version of the "IS-LM macroeconomic model leads to the system of equations: 1. 1 (r) = S(Y) 2.aY + L(r)...
Given the parallel plate shown below (a) Calculate the TEM mode circuit parameters (L',C',R',and G')step-by-step and compare your derivation to the answer given in Table 2 of Ludwig. Hint: Do this calculation carefully since a problem ofthis nature may show up on an exam with a different geometry. b) Now calculate these parameters for a copper-plate transmission line operating at 1 GHz. The geometry is w=6mm and d = 1 mm. The non-magnetic dielectric parameters are Er-2.25 and ơdiel 0.125...
The helicity operator is defined as h = sigma middot p/|p| where sigma = (sigma 0 0 sigma). Lets also define positive and negative helicity projection operators P^h_plusminus = (1 plusminus h)/2. Use natural units, h = c = 1. (a) By using the Dirac equation for a fermions with spinor u(p, s), mass m and energy E, show that P^h_plusminus = 1/2 (1 + gamma^5_|P| (E - beta m)). (b) For massless spin-1/2 particles like neutrino, show that the...
The ion Sm3 has 5 electrons in the f-shell. Determine the orbital (L), spin (S) total (J) angular momentum quantum number for this ion. of this ion The Lande's g factor is given by tplt 0 K f a salt containing 1 g mole 3J(J 1)+S(S +1)-L(L +1) 2J(J+1) and the susceptibility is 3KT where the symbols carry their usual meaning.
If the equation of motion of a small submarine is given by (m+200(0)-10 m/s, where fis a function of time depends on other parameters. For f- 0, determine 1) The standard form of equation of motion. 2) The time constant in terms of mass m 3) The maximum mass (m) that brings the speed to 0.5 m/s within 60 s. Use Fig. I If the submarine mass is one-half of the maximum mass obtained in 3, and a constant force...
In the given figure, the pipe entrance is sharp-edged. The elevation at the entrance is Az 44 m. If the flow rate is 0.004 m3/s, what power in Wis extracted by the turbine? For water at 20 "C, take p 998 kg/m3 and ? 0.001 kgm s. For cast on take ? ~ 0.26 mm. The minor loss coefficients are Entrance: 0.5; 5-cm 2 open globe valve: K-6.9 Take ?-227 For the given flow. take f 0.0316. Round the answer...