Search results for " Quantum Mechanics"
showing 10 items of 245 documents
Hen and egg problems of biology from TGD point of view
2022
Biology has several hen and egg problems. What came first: DNA,RNA, amino-acids or proto-cell membrane? Did metabolism precede genetic code or vice versa? The stimulus leading to this article could have been the finding that organic molecules are formed in interstellar space at ultralow temperatures of few Kelvin in which chemistry should freeze completely. Therefore the formation of glycine peptides, which has been demonstrated in the laboratory, should be impossible. The paradox disappears in the TGD framework as do also the hen and egg problems. Magnetic body carrying dark matter as $h_{eff}=nh_0$ phases allows a universal realization of genetic code and of the analogs of basic bio-molec…
Bi-coherent states as generalized eigenstates of the position and the momentum operators
2022
AbstractIn this paper, we show that the position and the derivative operators, $${{\hat{q}}}$$ q ^ and $${{\hat{D}}}$$ D ^ , can be treated as ladder operators connecting various vectors of two biorthonormal families, $${{{\mathcal {F}}}}_\varphi $$ F φ and $${{{\mathcal {F}}}}_\psi $$ F ψ . In particular, the vectors in $${{{\mathcal {F}}}}_\varphi $$ F φ are essentially monomials in x, $$x^k$$ x k , while those in $${{{\mathcal {F}}}}_\psi $$ F ψ are weak derivatives of the Dirac delta distribution, $$\delta ^{(m)}(x)$$ δ ( m ) ( x ) , times some normalization factor. We also show how bi-coherent states can be constructed for these $${{\hat{q}}}$$ q ^ and $${{\hat{D}}}$$ D ^ , both as con…
Construction of pseudo-bosons systems
2010
In a recent paper we have considered an explicit model of a PT-symmetric system based on a modification of the canonical commutation relation. We have introduced the so-called {\em pseudo-bosons}, and the role of Riesz bases in this context has been analyzed in detail. In this paper we consider a general construction of pseudo-bosons based on an explicit {coordinate-representation}, extending what is usually done in ordinary supersymmetric quantum mechanics. We also discuss an example arising from a linear modification of standard creation and annihilation operators, and we analyze its connection with coherent states.
Solving fractional Schroedinger-type spectral problems: Cauchy oscillator and Cauchy well
2014
This paper is a direct offspring of Ref. [J. Math. Phys. 54, 072103, (2013)] where basic tenets of the nonlocally induced random and quantum dynamics were analyzed. A number of mentions was maid with respect to various inconsistencies and faulty statements omnipresent in the literature devoted to so-called fractional quantum mechanics spectral problems. Presently, we give a decisive computer-assisted proof, for an exemplary finite and ultimately infinite Cauchy well problem, that spectral solutions proposed so far were plainly wrong. As a constructive input, we provide an explicit spectral solution of the finite Cauchy well. The infinite well emerges as a limiting case in a sequence of deep…
QCD analysis of the tau hadronic width
1992
32 páginas, 1 figura, 4 tablas.-- CERN-TH-6070-91 ; NUHEP-TH-91-8 ; PM-91-8.
and the electroweak penguin contribution
2003
Abstract Our dispersive sum rule calculation of the electroweak penguin contribution to ϵ′ ϵ is reviewed. A more recent analysis based on the finite-energy sum rule approach is described. Finally, a new determination of the electroweak penguin contribution to ϵ′ ϵ is presented.
The spin-dependent structure function of the proton g1p and a test of the Bjorken sum rule
2010
Abstract The inclusive double-spin asymmetry, A 1 p , has been measured at COMPASS in deep-inelastic polarised muon scattering off a large polarised NH3 target. The data, collected in the year 2007, cover the range Q 2 > 1 ( GeV / c ) 2 , 0.004 x 0.7 and improve the statistical precision of g 1 p ( x ) by a factor of two in the region x 0.02 . The new proton asymmetries are combined with those previously published for the deuteron to extract the non-singlet spin-dependent structure function g 1 NS ( x , Q 2 ) . The isovector quark density, Δ q 3 ( x , Q 2 ) , is evaluated from a NLO QCD fit of g 1 NS . The first moment of Δ q 3 is in good agreement with the value predicted by the Bjorken su…
QCD sum rule analysis of the pentaquark
2005
We perform a QCD sum rule calculation to determine the mass and the parity of the lowest lying pentaquark state. We include operators up to dimension $d=13$ in the OPE and the direct instanton contributions. We find evidence for a positive parity state. The contribution from operators of dimension $d>5$ is instrumental in determining the parity of the state and achieving the convergence of the sum rule.
From Hadronic τ Decays to the Chiral Couplings and
2009
A sum rule analysis of the hadronic τ -decay data can be used to determine the low-energy constants L 10 r ( μ ) and C 87 r ( μ ) . These constants are QCD chiral-order parameters, which appear at order p 4 and p 6 , respectively, in the chiral perturbation theory expansion of the V − A correlator. At order p 4 we obtain L 10 r ( M ρ ) = − ( 5.22 ± 0.06 ) ⋅ 10 − 3 . Including in the analysis the order p 6 contributions, we get L 10 r ( M ρ ) = − ( 4.06 ± 0.39 ) ⋅ 10 − 3 and C 87 r ( M ρ ) = ( 4.89 ± 0.19 ) ⋅ 10 − 3 GeV − 2 .
Results on longitudinal spin physics at COMPASS
2016
Abstract The COMPASS experiment at the CERN SPS has taken data for deep inelastic scattering of polarised muons off a polarised NH3 target in 2007 and 2011 and off a polarised 6LiD target in 2002–2004 and 2006. We present our new results on the longitudinal double spin asymmetry A 1 p and the spin-dependent structure function g 1 p obtained from the 2011 data set. These results are used in a NLO QCD fit to the world data to obtain the polarised parton distributions. Also an update on our results on the Bjorken sum rule, connecting the integral of the non-singlet spin-dependent structure function with the ratio of the weak coupling constants, is given. The gluon polarisation can be accessed …