Recent content by univector

Thanks for shedding the light on the cause to the change in the spin. So cooling the system is necessary, but not sufficient to maintain a 'long-time' coherence. For example, if the temperature is close to absolute zero, if two atoms are close, they may interact according to the joint...

If thermal motion (collision of atoms) changes the direction of an atom, will that change the direction of spin? If so, how much time does it take from the change in the atom orientation to the change in the spin?

By reversibility, if we turn the direction of the light propagation by 180 degrees, then the new propagation path follows the old propagation path. I suspect that when there is diffraction, the light propagation is not reversible?

Hi Dave, I was thinking about a modulated RF signal, whose frequency is not a spot but a range. How do we separate the RF signal into different frequency components? I suspect a series of transformers may do the job, but am not sure.

Is it possible to use a series of transformers to extract signal components of different frequencies simultaneously?

Fourier transform of RF signal with a "prism"? We can use a prism to decompose visible light into components of different frequencies. This is a Fourier transform by nature. For an ideal prism, the energy is conserved in the process. How about RF signals? There is no fundamental difference...

Hi Fredrik, Thanks for the explanation. If the matrix \rho is not diagonal, it is not trivial to calculate the matrix polynomial series. Instead, if we do a similary transform to diagonize \rho first, things may become easier. Let the diagonal matrix be D . Then by using the series...

I am confused by the definition of the Von Neumann entropy. In Nielson and Chung's book page 510, the Von Neumann entropy is defined as S (\rho) = - tr(\rho \log \rho) where \rho is the density matrix. What is the definition of the logrithm of a matrix? Is it some series expansion of a...

Fredrik, Thanks for the explanation, and I am with you now.

Fredrik and malawi_glenn, I am trying to reply to and comment on a few posts at once. Please let me know whether my understanding is right or wrong. Thanks. I am not sure if I understand situation 2 right. I think by "a single system in a specific but unknown state", the single system is...

Yes, you are right. An operator is usually Hermitian, but not necessarily unitary. The time evolution operator is unitary, being a sufficient condition for the probability preservation (=1). I am trying to figure out why the above relation is true. I think after a measurement of eigenstate...

Fredrik and malawi_glenn, I seem to understand a little better. I think the equation S_x |S_z+>=\frac{\hbar}{2}|S_z-> itself has nothing to do with any measurement. S_x represents a unitary transformation only. To measure an observable, we need a projective operator of that observable...

Got it. But what exactly does S_x |S_z+>=\frac{\hbar}{2}|S_z-> mean? Thanks.

Hi malawi_glenn, Thanks for your explanation. I understand what you said. What bothers me is: what does the equation \sigma_x |\sigma_z+>=|\sigma_z-> mean? According to Sakurai's book, applying any operator to a ket produces a new ket. Does the equation mean that after a measurement...

Mathematically, I understand the following eigen equation: A|a> = a |a>, where A is an operator, |a> is the eigenstate, and a is the eigenvalue. In terms of mathematics, it is nothing more than a linear transformation. However, physically, what does the equation mean? Is it equivalent to the...