Relativity of representations in quantum mechanics

Only the position representation is used in introductory quantum mechanics and the momentum representation is not usually presented until advanced undergraduate courses. To emphasize the relativity of the representations of the abstract formulation of quantum mechanics, two examples of representations related to the operators aX+(1-a)P and (XP+PX)/2 are presented.Comment: 10 pages, no figures, accepted in Am.J.Phy

Quantum mechanics in finite dimensional Hilbert space

The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with the infinite dimensional case. The construction of an unbiased basis for state determination is discussed.Comment: 14 pages, no figure

Entanglement for all quantum states

It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom, becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical relevance of the change of tensor product structure is mentioned.Comment: 9 page

EPR before EPR: a 1930 Einstein-Bohr thought experiment revisited

In 1930 Einstein argued against consistency of the time-energy uncertainty relation by discussing a thought experiment involving a measurement of mass of the box which emitted a photon. Bohr seemingly triumphed over Einstein by arguing that the Einstein's own general theory of relativity saves the consistency of quantum mechanics. We revisit this thought experiment from a modern point of view at a level suitable for undergraduate readership and find that neither Einstein nor Bohr was right. Instead, this thought experiment should be thought of as an early example of a system demonstrating nonlocal "EPR" quantum correlations, five years before the famous Einstein-Podolsky-Rosen paper.Comment: 11 pages, revised, accepted for publication in Eur. J. Phy

Efficiency diagnostic and advantages of procalcitonin and C-reactive protein in the early diagnosis of sepsis

The goal of our study is to assess the diagnostic profi tability of procalcitonin (PCT) in septic shock and another biomarker as C-reactive protein (CRP). Results: Fifty-four septic patients were assessed, 66% were males; mean age, 63 years. Eighty-eight percent was diagnosed as septic shock and 11% severe sepsis. Seventy-six percent were medical patients. Positive blood cultures in 42.5%. Sepsis origin: respiratory 46%, neurological 5%, digestive 37% and urinary 3%. Average SOFA score was 10.4. Conclusions: PCT and CRP have the same efficiency in early sepsis diagnosis. The PCT and CRP effi ciency diagnostic together is signifi cant but small. We suggest using both with the doubt of sepsis.Ye