Recent content by skynelson

And are there any other approaches to this argument that I am unaware of?

I am aware and well read on the decoherence approach to understanding how conglomerations of micro quantum systems will tend to lose quantum coherence via interaction with the environment. The cross terms in the density matrix for the system will tend to zero (due to the partial trace...

Gilbert Strang, Linear Algebra. I learned a ton from it.

Thank you for the clear thought provoking replies.

Suddenly I am at a loss with something I used to think I understood! From Consistent Quantum theory, Griffiths, pg 51: Our basis is |z+>, |z-> I can write |w+> = +cos(α/2)exp(-iθ/2) |z+> + sin(α/2)exp(iθ/2) |z-> In this case, if I choose α = π/2 and θ = π, then this |w+> points in...

Well, you have the right understanding as far as I can tell. Can you post the example in question? You haven't been too specific with your question.

Ok, great. So moving to an interpretational question: The mixed state doesn't have to be in diagonal form, but often is. (Right?) If it represents a collection of particles, then each diagonal entry (eigenvalue) squared can predict the likelihood of the particle we sample being in that...

Thanks for bringing me up to speed. I guess I hadn't been clear up until now on the distinction between the chosen basis, and the state of the system. Sounds like the state of the system is an objective quality of the system, and the basis states are arbitrarily chosen by me when describing the...

I would like to understand phase space better, spec. in relation to the quantum Liouville theorem. Can anyone point me to a decent online resource? I am most interested in conceptual understanding to begin with. Liouville's theorem says that if you follow a point in phase space, the number of...

Sorry I can't help you, but I would love to see Susskind's explanation of the Liouville theorem. This video lecture series on Stat Mech is very long...can you tell me which video has the part about Liouville? Thanks...

Right, ok. I was just thinking that you were saying that only a density matrix that represents a mixed state would have a set of mutually orthogonal eigenvectors. But here, you have confirmed that a pure state will (trivially) have orthogonal eigenvectors as well. Of course, I may still be...

This is probably my misunderstanding of the notation... The definition of a density matrix is in the attached file. (Sorry, the latex editor is not rendering properly when I preview my post). This definition is a sum over only one index 'j', which will invariably lead to a diagonal matrix...

Just to clarify, a pure state can typically be rewritten, using a change of basis, in diagonal form, right? But the new basis states will be superposition states. In that case, wouldn't the pure state thus written also have several mutually orthogonal eigenvectors (i.e. the new basis states)?

Ahh, I see. Very helpful, thanks. Is it true that a mixed state cannot be factored into a bra times a ket? Or in other words, it does not project onto a state, so it can't be written in the form |psi><psi|?

Thank you, that is helpful. So, then, if we form the projector: |K><K| = a^2|+>|d+><d+|<+| +...other terms (I have properly written the complex conjugate in reverse order) ...how do we move the <+| so it is next to the |+>? Clearly this is some simple linear algebra step I am missing.