How to Derive the Arbitrary Projection Operator
How to Derive the Arbitrary Projection Operator
Begin with a spin-1/2 quantum state pointing in some arbitrary direction n{\displaystyle {\mathbf {n} }}.
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Calculate Pn{\displaystyle P_{\mathbf {n} }} through matrix mechanics.
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Decompose the diagonal elements in terms of Pauli matrices.
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Decompose the off-diagonal elements in terms of Pauli matrices.
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Simplify the resulting expression.
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