(a) If C is orthogonal and M is symmetric, show that C−1MC is symmetric.(b) If C is orthogonal and M antisymmetric, show that C−1MC is antisymmetric
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A: Part (a): Consider N non-interacting particles are present in the system of volume V. Each particle…
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A: (1) [ z2, Lz] = [zz,Lz] = z[z,Lz] + [z,Lz]z But, [z,Lz] = 0 then,…
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A: The expectation value is given by exp μB B2kT - exp -μB B2kT 2 Cos h μB BkT= tan h μBB2 kT= tan h…
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Q: 4-21. Consider a lattice of M equivalent noninteracting magnetic dipoles, u (associated, say, with…
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A: Solution: The eigenfunction for the particle in a three-dimensional box is given by:…
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A: Step 1:To show that the property of antisymmetric remains unchanged under orthogonal similarity…
Q: (2) “Spin-1/2 particles" in magnetic field B can take energies E = (a) For N non-interacting…
A: The partition function of single particle is given by, Z1=∑ e-EkTZ1=e-µBBkT+eµBBkTZ1=2coshµBBkT…
Q: three-level system
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Q: (3) Let us assume that there are four distinguishable particles (A, B, C and D) and they occupy five…
A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…
(a) If C is orthogonal and M is symmetric, show that C−1MC is symmetric.
(b) If C is orthogonal and M antisymmetric, show that C−1MC is antisymmetric

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