# Pauli Matrices

1. Feb 18, 2013

### rupesh57272

Can any one tell me what is eigen value of product of a vector with pauli matrices i.e
A.σ where A is an arbitrary vector ?

2. Feb 18, 2013

### tiny-tim

welcome to pf!

hi rupesh57272! welcome to pf!

A.σ is a vector, so how does it have eigenvalues?

3. Feb 18, 2013

### dextercioby

He means a sort of 'scalar' product, which would be (after performing the sum) a 3x3 matrix which can have eigenvalues.

$$\vec{A}\cdot\vec{\sigma} = A_{x}\sigma_x + A_{y}\sigma_y + A_{z}\sigma_z$$.

4. Feb 18, 2013

### tiny-tim

ohh!!

then won't they be eigenspinors rather than eigenvectors, in the directions of ±A, and with eigenvalue |A| ?

5. Feb 18, 2013

### rupesh57272

Re: welcome to pf!

Sorry I forgot to mention that it is scalar product of a Vector and Pauli Spin matrices. What is the Eigen Value of it ?

6. Feb 18, 2013

### rupesh57272

I think it should be ±|A|

7. Feb 19, 2013

### tiny-tim

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)