WikiSysop: Created page with "So who's gotten part 3?? I'm confused about the value of mu (the scalar). I'm guessing that magnetic moment is equal to a Pauli spin multiplied by some sort of combination of..."

2022-08-31T22:40:06Z

Created page with "So who's gotten part 3?? I'm confused about the value of mu (the scalar). I'm guessing that magnetic moment is equal to a Pauli spin multiplied by some sort of combination of..."

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So who's gotten part 3??

I'm confused about the value of mu (the scalar). I'm guessing that magnetic moment is equal to a Pauli spin multiplied by some sort of combination of the basis. How exactly are they combined? I do not know. I think we're supposed to show that the 4x4 matrices given are representations of the 4 quantum states. How do we verify this, it seems like they're just combinations of the quantum states?! [[User:S44535078|S44535078]] 01:01, 3 November 2008 (PST)

<FONT COLOR=darkgreen> Here <math>\mu</math> is a scalar which, when multiplied by the scalar magnitude of the magnetic field ''B'', yields the scalar Zeeman energy ''E<SUB>Z</SUB>''. This scalar value is then multiplied into the spin operator (Pauli matrix, for spin 1/2) corresponding to the field direction -- generally the ''z'' direction, to keep things simple -- so <math>\sigma_3</math> -- to give the Zeeman part of the Hamiltonian operator (a matrix), which in turn operates on state vectors representing different quantum states. In the diagonal basis, the effect of this operator will be simply to multiply the state vector by the corresponding scaler energy eigenvalue. So for a simple spin 1/2 particle in a magnetic field along the ''z'' direction, <math>H_Z = \mu B \sigma_3</math> so that <math>H_Z \vert \uparrow \rangle = \mu B \vert \uparrow \rangle</math> and <math>H_Z \vert \downarrow \rangle = - \mu B \vert \downarrow \rangle</math>. Check it out. Then build a 4x4 version for the two-spin system. Although you can make a completely general version of the Zeeman Hamiltonian that does ''not'' assume that the magnetic field is along the ''z'' direction, it gains you nothing in the calculation of the Breit-Rabi eigenvalues, so I wouldn't bother. -- </FONT> [[User:Jess|Jess]] 09:42, 3 November 2008 (PST)

PHYS 210 ASSIGNMENT 8: HELP - Revision history

WikiSysop: Created page with "So who's gotten part 3?? I'm confused about the value of mu (the scalar). I'm guessing that magnetic moment is equal to a Pauli spin multiplied by some sort of combination of..."