Confinement, average forces, and the Ehrenfest theorem for a one-dimensional particle

The topics of confinement, average forces, and the Ehrenfest theorem are examined for a particle in one spatial dimension. Two specific cases are considered: (i) A free particle moving on the entire real line, which is then permanently confined to a line segment or ‘a box’ (this situation is achieved by taking the limit V ₀?→?∞ in a finite well potential). This case is called ‘a particle-in-an-infinite-square-well-potential’. (ii) A free particle that has always been moving inside a box (in this case, an external potential is not necessary to confine the particle, only boundary conditions). This case is called ‘a particle-in-a-box’. After developing some basic results for the problem of a particle in a finite square well potential, the limiting procedure that allows us to obtain the average force of the infinite square well potential from the finite well potential problem is re-examined in detail. A general expression is derived for the mean value of the external classical force operator for a particle-in-an-infinite-square-well-potential, $\hat{F}$ . After calculating similar general expressions for the mean value of the position ( $\hat{X}$ ) and momentum ( $\hat{P}$ ) operators, the Ehrenfest theorem for a particle-in-an-infinite-square-well-potential (i.e., $\mathrm{d}\langle\hat{X}\rangle/\mathrm{d}t=\langle\hat{P}\rangle/M$ and $\mathrm{d}\langle\hat{P}\rangle/\mathrm{d}t=\langle\hat{F}\rangle$ ) is proven. The formal time derivatives of the mean value of the position ( $\hat{x}$ ) and momentum ( $\hat{p}$ ) operators for a particle-in-a-box are re-introduced. It is verified that these derivatives present terms that are evaluated at the ends of the box. Specifically, for the wave functions satisfying the Dirichlet boundary condition, the results, $\mathrm{d}\langle\hat{x}\rangle/\mathrm{d}t=\langle\hat{p}\rangle/M$ and $\mathrm{d}\langle\hat{p}\rangle/\mathrm{d}t=\mathrm{b.t.}+\langle\hat{f}\rangle$ , are obtained where b.t. denotes a boundary term and $\hat{f}$ is the external classical force operator for the particle-in-a-box. Thus, it appears that the expected Ehrenfest theorem is not entirely verified. However, by considering a normalized complex general state that is a combination of energy eigenstates to the Hamiltonian describing a particle-in-a-box with v(x)?=?0 ( $\Rightarrow\hat{f}=0$ ), the result that the b.t. is equal to the mean value of the external classical force operator for the particle-in-an-infinite-square-well-potential is obtained, i.e., $\mathrm{d}\langle\hat{p}\rangle/\mathrm{d}t$ is equal to $\langle\hat{F}\rangle$ . Moreover, the b.t. is written as the mean value of a quantity that is called boundary quantum force, f _B. Thus, the Ehrenfest theorem for a particle-in-a-box can be completed with the formula $\mathrm{d}\langle\hat{p}\rangle/\mathrm{d}t=\langle{{f_\mathrm{B}}}\rangle$ .     

Nature-Inspired Routing and Wavelength Assignment Algorithms for Optical Circuit-Switched Polymorphic Networks

Polymorphic optical networks simultaneously support several optical switching paradigms over a single physical network. In this way, they provide service differentiation at the optical layer by employing the most appropriate paradigm for each service. One type of such architecture is the optical circuit-switched polymorphic network (OCSPN), which combines optical circuit switching paradigms with different grades of dynamism. The performance of this network relies on the utilization of efficient routing and wavelength assignment (RWA) algorithms. In this article, we review the fundamentals of OCSPNs and present a set of efficient RWA algorithms based on ant colony optimization and genetic algorithms.     

β-Na（Y_（1.5-x-y）Na_（0.5））F_6：Yb_xTm_y纳米颗粒的合成及其上转换发光性质

本文采用水热合成法制备了β-Na（Y1.5-x-yNa0.5）F6：YbxTmy（x=0.2~1.0,y=0.001~0.008）纳米颗粒,并利用X射线粉末衍射仪、透射电子显微镜和F-4600荧光分光光度计表征了其样品的物相、形貌和发光性质.结果表明样品物相为六角相,颗粒平均直径约22nm,并探讨了Yb3＋和Tm3＋掺杂浓度对样品的上转换发光性质的影响,结果表明敏化剂Yb3＋的最佳掺杂浓度为60%,而激活剂Tm3＋的最佳掺杂浓度为0.6%.     

Thermal conductivity of open‐cell polyolefin foams

The thermal conductivity and the cellular structure of novel open‐cell polyolefin foams produced by compression molding and based on blends of an ethylene‐vinyl acetate copolymer (EVA) and a low‐density polyethylene (LDPE) have been studied in the temperature range between 24 and 50 °C. The experimental results have shown that the cellular structure of the analyzed materials has interconnected cells because of the presence of large and small holes in the cell walls, this structure being clearly different to the typical structure of open‐cell polyurethane foams. It has been found that at low temperatures the materials have a slightly higher thermal conductivity than closed‐cell polyolefin foams of similar densities. The different mechanisms of heat flow, conduction, convection, and radiation have been analyzed by using experimental measurements and a theoretical model. It has been proved that, in spite of having an open‐cell structure, the convention mechanism is negligible, being the radiation mechanism the one which made different the conductivity of materials with varying cellular structures. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 212–221, 2008     

The decay of 91 min As

The energies and relative intensities of γ-rays following the β-decay of ⁷⁸As (and ⁷⁶As) to levels in ⁷⁸Se (and ⁷⁶Se) have been measured using an 8 cm³ Ge(Li) spectrometer. The β-decay of ⁷⁸As has been measured using a superconducting magnet beta-ray spectrometer with two 3 mm thick Si(Li) detectors. These data plus β-γ and γ-γ coincidence results have been used to construct a level scheme with 18 excited levels in ⁷⁸Se. The half-life of ⁷⁸As was measured to be 90.7±0.2 min.     

钒氧酞菁薄膜瞬态光电压性能的研究

本文分别用1064nm, 532nm和 355nm激发波长的YAG脉冲激光对所制备的phase Ⅱ结构钒氧酞菁膜Al\phase ⅡVOPc\ITO夹心电池进行瞬态光电压响应研究.随着3种波长激发光脉冲强度的增加, 瞬态光电压信号均增强. 激发光波长1064nm、532nm处于酞菁膜Q-带吸收区肩部, 光电压的极性与激发光入射方向无关, 均为负信号; 而激发光波长 355nm处于酞菁膜B-带, 光电压的极性与激发光入射方向有关, 从ITO极方向激发产生正电压信号, 从A1极激发产生负电压信号. 激发光波长对夹心电池的光电压产生有明显的作用, 光电压产生过程中应存在不同的机理. 这与前文^[1]对同一夹心电池稳态光电压响应研究所推断的结论一致.     

Dimethylalkoxygallanes: monomeric versus dimeric gas-phase structures

The molecular structures of the vapors produced on heating dimethylalkoxygallanes of the type [Me(2)Ga(OR)](2) have been determined by gas electron diffraction and ab initio molecular orbital calculations. In the solid state [Me(2)Ga(OCH(2)CH(2)NMe(2))](2) (1) and [Me(2)Ga(OCH(2)CH(2)OMe)](2) (2) adopt dimeric structures, although only the monomeric forms [Me(2)Ga(OCH(2)CH(2)NMe(2))] (1a) and [Me(2)Ga(OCH(2)CH(2)OMe)] (2a) were observed in the gas phase. For comparison the structure of the vapor produced on heating [Me(2)Ga(O(t)Bu)](2) (3) was also studied by gas electron diffraction. In contrast to 1 and 2, compound 3 is dimeric in the gas phase, as well as in the solid state. The gas-phase structures of 1a and 2a exhibit five-membered rings formed by a dative bond between Ga and the donor atom (N or O) from the donor-functionalized alkoxide. In 3 there is no possibility of a monomeric structure being stabilized by the formation of such a dative bond since only a monofunctional alkoxide is present in the molecule.     

Sequential Power-Dependence Theory

Existing methods for predicting resource divisions in laboratory exchange networks do not take into account the sequential nature of the experimental setting. We extend network exchange theory by considering sequential exchange. We prove that Sequential Power-Dependence Theory—unlike Power-Dependence Theory and most other exchange theories—has a unique point prediction for resource divisions in every network, and we show that these point predictions fare well in comparison to those from established theories.     

Relaxation Limit for Aw-Rascle System

We study the relaxation limit for the Aw-Rascle system of traffic flow. For this we apply the theory of invariant regions and the compensated compactness method to get global existence of Cauchy problem for a particular Aw-Rascle system with source, where the source is the relaxation term, and we show the convergence of this solutions to the equilibrium state.