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141.
SALVATORE DE VINCENZO 《Pramana》2013,80(5):797-810
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 $\mathrm{d}\langle\hat{p}\rangle/\mathrm{d}t=\langle{{f_\mathrm{B}}}\rangle$ . 相似文献
142.
A force field has been developed to describe the phase behaviour, interfacial, and transport properties of nitrogen and hydrocarbon mixtures under conditions relevant to those found in the high pressure extraction of oil from underground reservoirs. A Gibbs ensemble Monte Carlo method is used to parametrize intermolecular potentials for the pure components by matching experimental and simulated liquid and vapour coexisting densities. Also the surface tension, diffusion coefficient and shear viscosity of nitrogen and its mixtures with butane have been determined. The latter properties were obtained by canonical molecular dynamics simulations. The diffusion coefficient and shear viscosity were calculated by a Green-Kubo method. Results for pure nitrogen are given for temperatures ranging from 70 K to 110K. For mixtures of nitrogen with butane, results are presented at 339.4 K and 380.2 K. Good agreement is found between the results of simulations and available experimental data. 相似文献
143.
144.
Beales PA Bergstrom CL Geerts N Groves JT Vanderlick TK 《Langmuir : the ACS journal of surfaces and colloids》2011,27(10):6107-6115
We present a novel platform for investigating the composition-specific interactions of proteins (or other biologically relevant molecules) with model membranes composed of compositionally distinct domains. We focus on the interaction between a mitochondrial-specific lipid, cardiolipin (CL), and a peripheral membrane protein, cytochrome c (cyt c). We engineer vesicles with compositions such that they phase separate into coexisting liquid phases and the lipid of interest, CL, preferentially localizes into one of the domains (the liquid disordered (L(d)) phase). The presence of CL-rich and CL-depleted domains within the same vesicle provides a built-in control experiment to simultaneously observe the behavior of two membrane compositions under identical conditions. We find that cyt c binds strongly to CL-rich domains and observe fascinating morphological transitions within these regions of membrane. CL-rich domains start to form small buds and eventually fold up into a collapsed state. We also observe that cyt c can induce a strong attraction between the CL-rich domains of adjacent vesicles as demonstrated by the development of large osculating regions between these domains. Qualitatively similar behavior is observed when other polycationic proteins or polymers of a similar size and net charge are used instead of cyt c. We argue that these striking phenomena can be simply understood by consideration of colloidal forces between the protein and the membrane. We discuss the possible biological implications of our observations in relation to the structure and function of mitochondria. 相似文献
145.
M. Alvarez‐Lainez M. A. Rodriguez‐Perez J. A. DE Saja 《Journal of Polymer Science.Polymer Physics》2008,46(2):212-221
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 相似文献
146.
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%. 相似文献
147.
In this paper we solve the problemof desingularization of an absolutely isolatedsingularity of a differential equation, including thedicritical case. As an application, we prove thefiniteness of the number of dicritical points in theblowing up tree of an absolutely isolated singularity. 相似文献
148.
Joseph C. Calabrese 《有机化学》1993,(2)
The mechanism of decarboxylative cyclization of allylic cyclic carbamates 1 leading to 2-substituted △~3-piperidines and-pyrrolidines, as well as its applications to the total synthesis of (--)codonopsine, are described. 相似文献
149.
用75%乙醇回流法提取出藏药"西藏猫乳(生等)"的有效成分并浓缩精制后,采用HPLC梯度洗脱法,在选定的色谱条件{DuPont ZORBAX ODS C18色谱柱(4.6 mm×25 cm),用甲醇(A)-甲酸铵水溶液(pH=3.5,1.0 mL·min-1,B)进行梯度洗脱(甲醇浓度0~10 min,20%~25%;10~20 min,25%~40%;20~55 min,40%~55%;55~75 min,55%~75%;75~85 min,75%~90%),检测波长为290 am}下,对藏药"生等"的提取液进行了有效的分离与检测,并建立了"生等"药材的数字化色谱指纹谱(DFPS).所建立的方法能对藏药的产地归属进行有效的分辨. 相似文献
150.