Recent content by zhdx

The position and momentum are not positive definite. So the expectation of them can be positive, zero or negative. Similar observable includes the energy, which is dependent on the zero point we choose. However, the operator of the form ##A^\dagger A##, such as 'number' operator ##a^\dagger a##...

Thank you very much! Can we say that the operator of the form ##A^\dagger A## is a positive semidefinite operator?

Thanks you! Can you help me with the proof of the theorem you mentioned?

Thanks! Can this proof be generalized to the positive semidefinite case? That is, if all eigenvalues are non-negative, then the matrix is positive semidefinite.

Thanks for your reply. The measurement results of many operators can be negative. For example, the position and the momentum of a particle.

Thanks. I've read the proof for this specific case. What I mean is a more general case. For example, the operator ##(a^\dagger)^2 a^2 \sigma^\dagger\sigma## for a coupled cavity-atom system. Is the expectation for this operator always nonnegative for any state (include the mixed state)?

Thank you for your reply. It does so that the obervation result is nonnegative. I just want to find a mathematical proof.

Why does the expectation values of some operators, such as 'number' operator ##a^\dagger a## and atomic population operator ##\sigma^\dagger\sigma##, are always nonnegative? Can we prove this from a mathematical point? For example, are these operators positive semidefinite?

Does the ρ12 has relation to the population distributions? Thanks! Does the ρ12 has relation to the population distributions? Say consider two cases: Case 1: ρ11=0.9, ρ22=0.1 Case 2: ρ11=0.1, ρ22=0.2 What I've found is that the ρ12 in Case 2 is much less than in Case 1. (I've add a...

Consider we have a \Lambda type three level system, the one upper level is denoted by 3, and the two lower levels are denoted by 1 and 2. Assuming that the transitions between 1\leftrightarrow3 and 2\leftrightarrow3 are dipole alowed, while the transition between two lower states 1 and 2 is...

As we know that the properties of nanoscale material are quite diffrent from the bulk's. But what's the threshold of the size, or what the upper limmit where significant difference can be observed? The De Broglie wavelength or the Fermi wavelength of the electron in material? How to understand that?