Prove that if Ĥ is Hermitian, then the equation on the image is the adjoint of exp(-iĤ).

Q: A particle is freely moving in 3-d space such that E 2E, E:/2. (3.12) It's also known that it is…

A: The given relation is: E=Ex=2Ey=Ez2Ex=EEy=E/2Ez=2E Let the mass of the particle m px is expressed:…

Q: Consider a 1 nC charge at the origin of a 2D coordinate system. Calculate size of the electric field…

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Q: 4 Calculate the fraction of the power of a fundamental (1= m = 0) Gaussian beam that passes through…

A: The power of a beam passing through a circle of radius r and centered on the aperture is…

Q: m L = 1 {i² + (1+r)²a²} _K__ r ² 2 2 d L dt dr ƏL ər = mř − ma² (1 + r) + Kr = 0

A: We have to show,  Lagrangian in blue is equals the answer in pink

Q: (iii) Next let us modify the inner product space by introducing a weight function w(x) e-a and…

A: The normalisation of the function in this inner product space is given by:

Q: comes from our This equation, which of of constant acceleration can be put in yet another form which…

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Q: a) Let's say that it is chilly To outside, and a much warmer T; inside. If we were to have a…

A: Solution: a). (i). According to Fourier law, the flux of heat through the window is directly…

Q: Consider the similarity transform of a matrix a to A’ given A’ = S-1AS. You need to prove | A n | =…

A: as A'=S-1AStherefore1.    (A')n=S-1ASS-1ASS-1AS...........S-1AS       where the term in square…

Q: Volume of Brillouin zone. Show that the volume of the first Brillouin zone is (2π)³/Vc, where Vc is…

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Q: Show that the volume of the first Brillouin zone is 8³/V₁, where Vc is the volume of a crystal…

A: We will first define and write relation between reciprocal lattice vectors and direct lattice…