Search results for " Quantum Mechanics."
showing 10 items of 197 documents
First Measurement of the Gerasimov-Drell-Hearn Sum Rule forH1from 0.7 to 1.8 GeV at ELSA
2003
To verify the fundamental Gerasimov-Drell-Hearn (GDH) sum rule for the first time experimentally, we measured the helicity dependent total photoabsorption cross section with circularly polarized real photons and longitudinally polarized nucleons in the photon energy range 0.68-1.82 GeV with the tagged photon facility at ELSA. The experiment was carried out with a 4pi detection system, a circularly polarized tagged photon beam, and a frozen spin polarized proton target. The contribution to the GDH sum rule in this photon energy range is [49.9+/-2.4(stat)+/-2.2(syst)] mub.
Sum rules across the unpolarized Compton processes involving generalized polarizabilities and moments of nucleon structure functions
2018
We derive two new sum rules for the unpolarized doubly virtual Compton scattering process on a nucleon, which establish novel low-$Q^2$ relations involving the nucleon's generalized polarizabilities and moments of the nucleon's unpolarized structure functions $F_1(x,Q^2)$ and $F_2(x,Q^2)$. These relations facilitate the determination of some structure constants which can only be accessed in off-forward doubly virtual Compton scattering, not experimentally accessible at present. We perform an empirical determination for the proton and compare our results with a next-to-leading-order chiral perturbation theory prediction. We also show how these relations may be useful for a model-independent …
The SVZ plasmon
1985
The sum rule technique of Shifman, Vainshtein and Zakharov is applied to a non-relativistic many-body system, the homogeneous, degenerate electron gas. The operator product expansion for the nonrelativistic correlation function is derived and shown to be equivalent in lowest order to a moment expansion. The nonperturbative terms in this expansion characterize the interacting ground state (“vacuum”) of the system. For the electron gas they can be related to the correlation energy which is very well known. Following as close as possible the SVZ procedure the mass of the plasmon (i.e. the dispersion coefficient of the collective plasma excitation) is calculated and compared with results from c…
Quantum Mechanics of Point Particles
2013
In developing quantum mechanics of pointlike particles one is faced with a curious, almost paradoxical situation: One seeks a more general theory which takes proper account of Planck’s quantum of action \(h\) and which encompasses classical mechanics, in the limit \(h\rightarrow 0\), but for which initially one has no more than the formal framework of canonical mechanics. This is to say, slightly exaggerating, that one tries to guess a theory for the hydrogen atom and for scattering of electrons by extrapolation from the laws of celestial mechanics. That this adventure eventually is successful rests on both phenomenological and on theoretical grounds.
Integrated photoabsorption strength and sum rules for a bound Dirac particle
1985
Relativistic effects in the integrated total photoabsorption cross section are discussed using a simple model of a Dirac particle bound in a central potential of scalar or vector type. The integrated strength is calculated explicitly and compared to a new relativistic extension of the TRK-sum rule using positive energy projection and to predictions from dispersion relations. M1 and E2 sum rules are also considered. In all cases the integrated strength exceeds the classical sum rule up to a few percent. The dispersion sum rule cannot be compared directly to the integrated strength since it contains a negative contribution from pair production in the potential field which is of the order of a…
Muonic-hydrogen Lamb shift: Dispersing the nucleon-excitation uncertainty with a finite-energy sum rule
2013
We assess the two-photon exchange contribution to the Lamb shift in muonic hydrogen with forward dispersion relations. The subtraction constant (T) over bar (0, Q(2)) that is necessary for a dispersive evaluation of the forward doubly virtual Compton amplitude, through a finite energy sum rule, is related to the fixed J = 0 pole generalized to the case of virtual photons. We evaluated this sum rule using excellent virtual photoabsorption data that are available. We find that the "proton polarizability correction" to the Lamb shift in muonic hydrogen is -(40 +/- 5) mu eV. We conclude that nucleon structure-dependent uncertainty by itself is unlikely to resolve the large (300 mu eV) discrepan…
Computing the dipole polarizability of 48Ca with increased precision
2018
We compute the electric dipole polarizability of 48Ca with an increased precision by including more correlations than in previous studies. Employing the coupled-cluster method we go beyond singles and doubles excitations and include leading-order three-particle-three-hole (3p-3h) excitations for the ground state, excited states, and the similarity transformed operator. We study electromagnetic sum rules, such as the bremsstrahlung sum rule m_0 and the polarizability sum rule alpha_D using interactions from chiral effective field theory. To gauge the quality of our coupled-cluster approximations we perform several benchmarks with the effective interaction hyperspherical harmonics approach in…
Susy for non-Hermitian Hamiltonians, with a view to coherent states
2020
We propose an extended version of supersymmetric quantum mechanics which can be useful if the Hamiltonian of the physical system under investigation is not Hermitian. The method is based on the use of two, in general different, superpotentials. Bi-coherent states of the Gazeau-Klauder type are constructed and their properties are analyzed. Some examples are also discussed, including an application to the Black-Scholes equation, one of the most important equations in Finance.
The Kadanoff–Baym approach to double excitations in finite systems
2011
We benchmark many-body perturbation theory by studying neutral, as well as non-neutral, excitations of finite lattice systems. The neutral excitation spectra are obtained by time-propagating the Kadanoff-Baym equations in the Hartree-Fock and second Born approximations. Our method is equivalent to solving the Bethe-Salpeter equation with a high-level kernel while respecting self-consistently, which guarantees the fulfillment of a frequency sum rule. As a result, we find that a time-local method, such as Hartree-Fock, can give incomplete spectra, while already the second Born, which is the simplest time-nonlocal approximation, reproduces well most of the additional excitations, which are cha…
Examples of pseudo-bosons in quantum mechanics
2010
We discuss two physical examples of the so-called {\em pseudo-bosons}, recently introduced in connection with pseudo-hermitian quantum mechanics. In particular, we show that the so-called {\em extended harmonic oscillator} and the {\em Swanson model} satisfy all the assumptions of the pseudo-bosonic framework introduced by the author. We also prove that the biorthogonal bases they produce are not Riesz bases.