rupesh57272
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Can anyone tell me what is eigen value of product of a vector with pauli matrices i.e
A.σ where A is an arbitrary vector ?
A.σ where A is an arbitrary vector ?
Finding the Eigen Value of A.σ Vector Product
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welcome to pf!
hi rupesh57272! welcome to pf!
i don't follow you
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hi rupesh57272! welcome to pf!
i don't follow you
…A.σ is a vector, so how does it have eigenvalues? 
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He means a sort of 'scalar' product, which would be (after performing the sum) a 3x3 matrix which can have eigenvalues.
[tex]\vec{A}\cdot\vec{\sigma} = A_{x}\sigma_x + A_{y}\sigma_y + A_{z}\sigma_z[/tex].
[tex]\vec{A}\cdot\vec{\sigma} = A_{x}\sigma_x + A_{y}\sigma_y + A_{z}\sigma_z[/tex].
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ohh!
then won't they be eigenspinors rather than eigenvectors, in the directions of ±A, and with eigenvalue |A| ?
then won't they be eigenspinors rather than eigenvectors, in the directions of ±A, and with eigenvalue |A| ?
rupesh57272
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Sorry I forgot to mention that it is scalar product of a Vector and Pauli Spin matrices. What is the Eigen Value of it ?
rupesh57272
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I think it should be ±|A|
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sorry, yes, ±|A|
eg for Sz, or for S-z, the two eigenspinors are the same …
spinor in the z direction (which we call spin-up, with positive eigenvector, for Sz and spin-down, with negative eigenvector, for S-z)
spinor in the minus-z direction (which we call spin-down, with negative eigenvector, for Sz and spin-up, with positive eigenvector, for S-z)
spinor in the z direction (which we call spin-up, with positive eigenvector, for Sz and spin-down, with negative eigenvector, for S-z)
spinor in the minus-z direction (which we call spin-down, with negative eigenvector, for Sz and spin-up, with positive eigenvector, for S-z)