http://cds.cern.ch/record/262851/files/9405029.pdf

Supersymmetry and quantum mechanics

There is a special reason for reviewing this book at this time: it is the 50th edition of a compendium that is known and used frequently in most chemical and physical laboratories in many parts of the world. Surely, a publication that has been published for 56 years, withstanding the vagaries of science in this century, must have had something to offer. There is another reason: while the book is a standard fixture in most chemical and physical laboratories, including those in medical centers, it is not as frequently seen in the laboratories of physician's offices (those either in solo or group practice). I believe that the Handbook can be useful in those laboratories. One of the reasons, among others, is that the various basic items of information it offers may be helpful in new tests, either physical or chemical, which are continuously being published. The basic information may relate

Handbook of Chemistry and Physics

The Young's modulus (E) of a material is a key parameter for mechanical engineering design. Silicon, the most common single material used in microelectromechanical systems (MEMS), is an anisotropic crystalline material whose material properties depend on orientation relative to the crystal lattice. This fact means that the correct value of E for analyzing two different designs in silicon may differ by up to 45%. However, perhaps, because of the perceived complexity of the subject, many researchers oversimplify silicon elastic behavior and use inaccurate values for design and analysis. This paper presents the best known elasticity data for silicon, both in depth and in a summary form, so that it may be readily accessible to MEMS designers.

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What is the Young's Modulus of Silicon?

Recent progress1,2,3 in the synthesis of high-quality single-walled carbon nanotubes4 (SWNTs) has enabled the measurement of their physical and materials properties5,6,7,8. The idea that nanotubes might be integrated with conventional microstructures to obtain new types of nanoscale devices, however, requires an ability to synthesize, isolate, manipulate and connect individual nanotubes. Here we describe a strategy for making high-quality individual SWNTs on silicon wafers patterned with micrometre-scale islands of catalytic material. We synthesize SWNTs by chemical vapour deposition of methane on the patterned substrates. Many of the synthesized nanotubes are perfect, individual SWNTs with diameters of 1–3 nm and lengths of up to tens of micrometres. The nanotubes are rooted in the islands, and are easily located, characterized and manipulated with the scanning electron microscope and atomic force microscope. Some of the SWNTs bridge two metallic islands, offering the prospect of using this approach to develop ultrafine electrical interconnects and other devices.

Synthesis of individual single-walled carbon nanotubes on patterned silicon wafers

Handbook of SiC properties for fuel performance modeling

The following two equations are proposed for the temperature dependence of the elastic stiffness constants: ${c}_{\mathrm{ij}}={c}_{\mathrm{ij}}^{0}\ensuremath{-}\frac{s}{({e}^{\frac{t}{T}}\ensuremath{-}1)}$ and ${c}_{\mathrm{ij}}=a\ensuremath{-}\frac{b{T}^{2}}{(T+c)}$, where ${c}_{\mathrm{ij}}^{0}$, $s$, $t$, $a$, $b$, and $c$ are constants. The applicability of these two equations and that of Wachtman's equation is examined for 57 elastic constants of 22 substances. The first equation has a theoretical justification and gives the best over-all results. Neither of the three equations give the theoretically expected ${T}^{4}$ dependence at low temperatures, and therefore they are not expected to give very accurate results at very low temperatures ($\ensuremath{\lesssim}\frac{{\ensuremath{\Theta}}_{D}}{50}$). A new melting criterion is also examined.

Temperature Dependence of the Elastic Constants

A detailed study of the bound-state properties of the Hulth\'en potential is presented. Accurate eigenenergies are obtained for the Hulth\'en potential by numerical integration of the Schr\"odinger equation. One-parameter variational calculations are carried out. The variational results are practically identical to the exact energies, except in the high-screening region. The critical screening parameter is calculated for various values of l for n\ensuremath{\le}10 by a numerical solution of the wave equation. The energy eigenvalues obtained by a variety of methods are compared and discussed. The variational wave functions are employed to calculate absorption oscillator strengths for 1s\ensuremath{\rightarrow}2p, 1s\ensuremath{\rightarrow}3p, and 2p\ensuremath{\rightarrow}3d transitions.

Eigenenergies and oscillator strengths for the Hulthén potential.

Energies of s Eigenstates in a Static Screened Coulomb Potential

A number of properties of the bound eigenstates of an electron in an exponential cosine screened Coulomb potential, $V(\mathcal{r})=\ensuremath{-}(\frac{{e}^{2}}{\ensuremath{\kappa}\mathcal{r}}){e}^{\ensuremath{-}qr}cos(q\mathcal{r})$, are studied. Perturbation and variation methods are used to calculate the eigenvalues. Detailed results are presented for the first four $s$ states. For each state there is a critical value of the screening parameter ${\ensuremath{\delta}}_{c}$ above which no bound states with negative energy exist. The value of ${\ensuremath{\delta}}_{c}$ for the ground state is obtained from a two-parameter variational calculation. The total number of different energy levels is finite for any value of the screening parameter $\ensuremath{\delta}$ greater than zero, and is found to be approximately linearly dependent on $\frac{1}{{\ensuremath{\delta}}_{c}}$, The square of the number of bound $s$ states is also shown to be linear with $\frac{1}{{\ensuremath{\delta}}_{c}}$, Positive-energy states are also discussed.

Bound eigenstates of the exponential cosine screened coulomb potential.

The method of shifted large-N expansion, where N is the number of spatial dimensions, is applied to study the bound states of the Hellmann potential, which represents the superposition of the attractive Coulomb potential (-A/r) and the Yukawa potential B exp(-Cr)/r of arbitrary strength B and screening parameter C It emerges that although the analytic expressions for the energy eigenvalues ${E}_{n}$,l yield quite accurate results for a wide range of n,l in the limit of very weak screening, the results become gradually worse as the strength B and the screening coefficient C increase This happens due to the fact that the effective large-N potential becomes quite shallow in comparison to the true potential and the expansion parameter is not sufficiently small enough to guarantee the convergence of the expansion series for the energy levels Furthermore, the present analysis reveals an intrinsic limitation of the technique in case of specific superposition of potentials: For certain choices of B, C, n, and l, the structure of the effective potential becomes such that it does not possess a local minimum and consequently the method turns out to be inapplicable to determining the corresponding bound-state energies However, such a limitation does not persist for a simple screened Coulomb potential and reasonably accurate energy eigenvalues and bound-state normalizations are obtained for the neutral atoms It is expected that the normalized bound-state wave functions obtained through the shifted large-N formalism may be useful in calculating the oscillator strength, bound-bound dipole transition matrix elements, etc which have significant importance in atomic processes

Y. P. Varshni

Papers

Temperature Dependence of the Elastic Constants

Eigenenergies and oscillator strengths for the Hulthén potential.

Energies of s Eigenstates in a Static Screened Coulomb Potential

Bound eigenstates of the exponential cosine screened coulomb potential.

Shifted large-N expansion for the bound states of the Hellmann potential.