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.     

Nonlinear quantum mechanics,the superposition principle,and the quantum measurement problem

There are four reasons why our present knowledge and understanding of quantum mechanics can be regarded as incomplete. (1) The principle of linear superposition has not been experimentally tested for position eigenstates of objects having more than about a thousand atoms. (2) There is no universally agreed upon explanation for the process of quantum measurement. (3) There is no universally agreed upon explanation for the observed fact that macroscopic objects are not found in superposition of position eigenstates. (4) Most importantly, the concept of time is classical and hence external to quantum mechanics: there should exist an equivalent reformulation of the theory which does not refer to an external classical time. In this paper we argue that such a reformulation is the limiting case of a nonlinear quantum theory, with the nonlinearity becoming important at the Planck mass scale. Such a nonlinearity can provide insights into the aforesaid problems. We use a physically motivated model for a nonlinear Schr?dinger equation to show that nonlinearity can help in understanding quantum measurement. We also show that while the principle of linear superposition holds to a very high accuracy for atomic systems, the lifetime of a quantum superposition becomes progressively smaller, as one goes from microscopic to macroscopic objects. This can explain the observed absence of position superpositions in macroscopic objects (lifetime is too small). It also suggests that ongoing laboratory experiments may be able to detect the finite superposition lifetime for mesoscopic objects in the near future.     

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.     

钙钛矿结构荧光材料MZrO3:Eu3+,A (M=Ca2+, Ba2+; A=Li+, Na+, K+)的制备及其发光性质

Calcium and barium zirconate powders based upon CaZrO₃:Eu³⁺,A and BaZrO₃:Eu³⁺,A (A=Li⁺, Na⁺, K⁺) were prepared by combustion synthesis method and heating to ~1000℃ to improve crystallinity.The structure and morphology of materials were examined by X-ray diffraction (XRD) and scanningelectron microscopy (SEM). XRD results showed that CaZrO₃:Eu³⁺,A and BaZrO₃:Eu³⁺,A (A=Li⁺, Na⁺, K⁺) perovskites possessed orthorhombic and cubic structures, respectively. The morphologies of all powderswere very similar consisting of small, coagulated, cubical particles with narrow size distributions andsmooth and regular surfaces. The characteristic luminescences of Eu³⁺ ions in CaZrO₃:Eu³⁺,A (A=Li⁺, Na⁺, K⁺) lattices were present with strong emissions at 614 and 625 nm for ⁵D₀→⁷F₂ transitions with other weakeremissions observed at 575, 592, 655, and 701 nm corresponding to ⁵D₀→⁷F_n transitions (where n=0, 1, 3, 4 respectively). In BaZrO₃:Eu³⁺ both the ⁵D₀→⁷F₁ and ⁵D₀→⁷F₂ transitions at 595 and 613 nm were strong.Photoluminescence intensities of CaZrO₃:Eu³⁺ samples were higher than those of BaZrO₃:Eu³⁺ lattices. Thisremarkable increase of photoluminescence intensity (corresponding to ⁵D₀→⁷F_n transitions) was observedin CaZrO₃:Eu³⁺ and BaZrO₃:Eu³⁺ if co-doped with Li⁺ ions. An additional broad band composed of manypeaks between 440 to 575 nm was observed in BaZrO₃:Eu³⁺,,A samples. The intensity of this band wasgreatest in Li⁺ co-doped samples and lowest for K⁺ doped samples.     

镍铁氰化物纳米粒子的合成及其多相催化无溶剂条件下苯甲醇氧化的潜能(英文)

Nickel hexacyanoferrate nanoparticles were synthesized and characterized using elemental analysis, thermal analysis, infrared spectroscopy, and X-ray diffraction. A FE-SEM image of the nickel hexacyanoferrate showed that it consists of nearly spherical particles with sizes ranging from 30 to 70 nm. The synthesized material was found to be a heterogeneous catalyst useful for the solvent-free oxidation of benzyl alcohol with H2O2 as an oxidant. A 36% conversion of benzyl alcohol to benzaldehyde was achieved under optimized reaction conditions using specific parameters such as the amount of catalyst, the temperature, the benzyl alcohol to H2O2 molar ratio, and the reaction time.