classes:2009:fall:phys4101.001:lec_notes_1130
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| classes:2009:fall:phys4101.001:lec_notes_1130 [2009/12/06 16:42] – ely | classes:2009:fall:phys4101.001:lec_notes_1130 [2009/12/06 16:54] (current) – ely |
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| So we missed the <math>(S_1)^2</math> and <math>(S_2)^2</math> terms which bring: | So we missed the <math>(S_1)^2</math> and <math>(S_2)^2</math> terms which bring: |
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| <math>(S_1)^2+(S_2)^2= \frac{1}{2}\hbar^2 \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix} </math> | <math>\frac{1}{2}\hbar^2 \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix} </math> |
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| which gives | which gives us the <math>J^2</math> matrix: |
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| <math>J^2 = \frac{1}{2}\hbar^2 \begin{pmatrix} 4 & 0 & 0 & 0 \\ 0 & 2 & 3 & 0 \\ 0 & 3 & 2 & 0 \\ 0 & 0 & 0 & 4 \end{pmatrix} </math> | <math>J^2 = \frac{1}{2}\hbar^2 \begin{pmatrix} 4 & 0 & 0 & 0 \\ 0 & 2 & 3 & 0 \\ 0 & 3 & 2 & 0 \\ 0 & 0 & 0 & 4 \end{pmatrix} </math> |
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| | We then found some of the Eigenvalues and Eigenstates of <math>2(S_1)(S_2)</math> |
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| | <math> \begin{pmatrix} 1-{\lambda} & 0 & 0 & 0 \\ 0 & -1-{\lambda} & 2 & 0 \\ 0 & 2 & -1-{\lambda} & 0 \\ 0 & 0 & 0 & 1-{\lambda} \end{pmatrix} </math> |
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| | more will be coming when i figure out how to make arrows |
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| ((Please try to include the following | ((Please try to include the following |
classes/2009/fall/phys4101.001/lec_notes_1130.1260139349.txt.gz · Last modified: 2009/12/06 16:42 by ely