On solving the Schrödinger equation for a complex deictic potential in one dimension

Making use of an ansatz for the eigenfunction, we investigate closed-form solutions of the Schrödinger equation for an even power complex deictic potential and its variant in one dimension. For this purpose, extended complex phase-space approach is utilized and nature of the eigenvalue and the corresponding eigenfunction is determined by the analyticity property of the eigenfunction. The imaginary part of the energy eigenvalue exists only if the potential parameters are complex, whereas it reduces to zero for real coupling parameters and the result coincides with those derived from the invariance of Hamiltonian under \(\mathcal {P}\mathcal {T}\) operations. Thus, a non-Hermitian Hamiltonian possesses real eigenvalue, if it is \(\mathcal {P}\mathcal {T}\) -symmetric.     

A Cutting-Point Technique For Solving Nonlinear State Regulator Problems

In this paper, we present a technique for solving an optimizationproblem of Lagrange type where the system equations are stiffand the system can be expressed explicitly in terms of a singular-perturbationparameter. Such problems arise in control theory and in otherapplication areas. The proposed procedure consists of solvingthe singularly perturbed two-point boundary-value problem comprisedby the coupled state and adjoint equations arising from thefirst-order necessary conditions for optimality. It is assumedthat the coupled system has no turning points, and the solutionis accomplished by making an analytic stretching in the boundarylayers to give three explicit boundary-value problems whichare treated separately. The novel feature of the procedure isthat the explicit boundary conditions for each problem are obtained,at the selected cut points, from the solution to the reducedproblem. The application of the procedure is described for twoexamples.     

Transport of Neutral Arenes through an Aqueous Barrier by Resorcinol–Aldehyde Tetramers

The transportation of neutral arenes such as benzene, toluene, o,m,p-xylene, durene,biphenyl, anthracene and phenanthrene through an aqueous medium using the crownconformation of tetrameric cyclophane hosts 1 and 2 has been studied. In general,transportation of all arenes increases with time, exceptfor toluene, which showssaturation behaviour with both hosts 1 and 2.Among the larger arenes, transportationof biphenyl is a maximum with 1; with host 2,transportation of anthracene is a maximumdue to its larger association constant. In the case ofsmaller arenes, 1 transportsbenzene most effectively, and transportation decreases asthe number of methyl groups onbenzene increases, showing that stereoelectronic factors affecttransportation. With 2toluene is transported most effectively due tothe change in the shape of the binding cavitycaused by a change in bridging groups. A comparison oftransportation for 1 h with 1 and 2shows that for all arenes transportation is greater withhost 2 than with 1 due to thehydrophobic nature of 2.     

Drell–Yan process at Large Hadron Collider

Drell–Yan process at LHC, q[`(q)]? Z/g^* ? l⁺l^-q\bar {q}\to Z/\gamma ^\ast \to \ell ^+\ell ^-, is one of the benchmarks for confirmation of Standard Model at TeV energy scale. Since the theoretical prediction for the rate is precise and the final state is clean as well as relatively easy to measure, the process can be studied at the LHC even at relatively low luminosity. Importantly, the Drell–Yan process is an irreducible background to several searches of beyond Standard Model physics and hence the rates at LHC energies need to be measured accurately. In the present study, the methods for measurement of the Drell–Yan mass spectrum and the estimation of the cross-section have been developed for LHC operation at the centre-of-mass energy of 10 TeV and an integrated luminosity of 100 pb^− 1 in the context of CMS experiment.     

Systematic study of multiparticle production in nucleus–nucleus interactions at 14.6 A GeV

An experimental analysis of 855 events induced by 14.6 A GeV ²⁸Si in nuclear emulsion is presented. Mean multiplicities of charged secondary particles produced in the nuclear interactions are studied and compared with the results from the other experiments for the same projectile at 3.7 A GeV as well as data for proton at similar energy (14 GeV). An analysis of pseudorapidity densities of target fragments (black and grey particles) is also performed. The behaviour of the KNO scaling law of the multiplicity distribution for shower particles has been examined. In order to accumulate knowledge about the intermittent behaviour of shower particles, the scaled factorial moments (SFMs) are computed in η-space and ?-space for a set of data in the ²⁸Si–AgBr events. Furthermore, validity of limiting fragmentation of shower particles produced in central collision events induced by ²⁸Si-emulsion interactions has been tested. A crude estimation for the energy density of the nuclear matter formed in the central collision events at our energy has been examined.