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Representing spin operators in alternate basis
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[QUOTE="blue_leaf77, post: 5449805, member: 536596"] Which eigenvectors are they, ##S_x##, ##S_y##, or ##S_z##? Find out ##S_x## in matrix form in the basis of the eigenvectors of ##S_z## (this is the most common form found in any literature) then find its eigenvalues as well as its eigenvectors (in the basis of the eigenvectors of ##S_z##). The operator equations you wrote above are the action on an eigenvector of ##S_z##. Moreover, the forms of those equation are in the basis-free, operator forms, therefore no matter which basis you chose the form of the above equations will not change. However, if you redefine the notation ##|s,m_s\rangle## to be the eigenvector of ##S_x##, then those equations will indeed look different. It's not clear to me which method you were referring to. To be honest, in matrix form I know no other way to transform a matrix from one basis into another one unless using the usual similarity transformation. [/QUOTE]
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Representing spin operators in alternate basis
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