Show explicitly that the alpha matrices are Hermitian.
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Show explicitly that the alpha matrices are Hermitian. Do this in Dirac-Pauli representation.
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- Show that   for any operator  is positive.Consider the special shape pictured in the diagram below. It is a cylinder, centered on the origin with its axis oriented along z, and it has been partially hollowed to leave two cone-shaped cavities at the top and bottom of the cylinder. The radius of the object is a, its height is 2a, and the solid part of the object (the shaded region that is visible in the rightmost panel of the illustration above, which shows a drawing of the cross-section of the object) has a uniform volume charge density of po. Assume that the object is spinning counter clockwise about its cylinder axis at an angular frequency of w. Which of the following operations is part of the calculation of the magnitude of the current density that is associated with the motion of the rotating object as a function of r (select all that apply)?Need B and C.
- Consider the following operators on a Hilbert space V³ (C): 0-i 0 ABAR-G , Ly i 0-i , Liz 00 √2 0 i 0 LE √2 010 101 010 What are the corresponding eigenstates of L₂? 10 00 0 0 -1 What are the normalized eigenstates and eigenvalues of L₂ in the L₂ basis?A spherical shell of radius R centered about the origin carrying a uniform surface charge o spins at an angular velocity o = (ê sin y +î cos y) w. To evaluate the vector potential A(0,0, z) (coordinates in Cartesian coordinates) in Coulomb gauge, we %3D can evaluate 27 Ã(0,0,2) = / « dcos 0' o' dợ'R*Ÿ (e', o') (1) where one recognizes dcos 0'do'R² as an area element on the spherical shell. What is Ý before doing any of the integration? [Express your answer in terms of {@,e', ø', y,R, z,£, §, ¿}].(a) Using Dirac notation, write down the definition of a projection operator and that of a density operate and state the differences between the two.
- The essence of the statement of the uniqueness theorem is that if we know the conditions the limit that needs to be met by the potential of the system, then we find the solution of the system , then that solution is the only solution that exists and is not other solutions may be found. If we know potential solutions of a system, can we determine the type of system that generate this potential? If so, prove the statement! If no, give an example of a case that breaks the statement!For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential function f (that is, ∇f=F). F(x,y)=(−3siny)i+(10y−3xcosy)j