Interbasis expansions for isotropic harmonic oscillator

The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n.     

变形谐振子势的能谱方程

讨论了3种变形谐振子势:左右两边不同参数的谐振子势、左边方形势加右边谐振子势和谐振子势中间加δ势中的能量本征态函数.这些函数都可以由厄米函数表示.由波函数及其一次导数在原点的衔接条件,得到了能谱方程.     

On the derivation of the entropy of ideal quantum gases confined in a three-dimensional harmonic potential

In this work,the entropy functions of ideal quantum gases in a three-dimensional harmonic trap are analytically calculated using temperature as an explicit variable.Afterward,the applicability of the analytical formulas is validated by comparison with the numerical calculation.The results illustrate that the obtained functions could be applied for the whole temperature regime with a maximum relative deviation of less than 7.5%in the vicinity of the critical temperature Tcin the case of Bose gases.Meanwhile,for Fermi gases,although the analytical formula fits well at very low-and high-temperature regimes,it cannot be applied at temperature in the range[0.3-0.5]T_F,where T_F is the Fermi temperature.In addition,the consistency between our formulas and classical ones at significantly high temperatures is also discussed.     

The support designs of the triply even binary codes of length 48

In this paper, we present examples of codes all of whose weight classes support 1‐designs, with duals whose classes include two that support 2‐designs. We can find these examples in the triply even binary codes of length 48, which have been classified by Betsumiya and Munemasa.     

Structural,magnetic and optical properties of two concomitant molecular crystals

A new 1D complex has been prepared and characterized. X-ray single crystal structure confirms that the Cu(II) ions assemble in alternating chains with Cu … Cu distances of 2.5685(4) and 3.1760(4) Å. The temperature dependence of the magnetic susceptibility reveals an antiferromagnetic interaction between the paddle-wheel copper centers with an exchange of −300 cm⁻¹. The exchange integral was also determined by quantum chemical ab-initio calculations, using polarised and unpolarised basis sets reproducing well the experimental value. The second harmonic generation efficiency of a concomitantly crystallized material was evaluated and was found to be comparable to urea.     

A Microcell for Stripping Analysis with Glassy Carbon and Mercury-Plated Glassy Carbon Electrodes

Abstract

A microcell has been constructed for stripping analysis in solution volumes as low as 5 μl, employing a glassy carbon or mercury-plated glassy carbon working electrodes and a three electrode system. Using normal d.c. stripping techniques, as little as 100 picograms of mercury and 10 picograms of lead can be determined. With the more sensitive second harmonic a.c. voltammetric technique, this limit is lowered to 10 picograms of mercury and 1 picogram of lead.     

不均匀场中氢分子离子高次谐波产生的理论研究

在非Born-Oppenheimer近似下，通过求解含时薛定谔方程的方法，对氢分子离子在不均匀场中高次谐波的产生进行了理论研究.计算结果显示，同均匀场相比，电离的电子在不均匀场中加速会获得更多的能量，从而更有利于得到宽频谱.此外,通过优化不均匀场中的空间不均匀度，长量子路径被明显的抑制，最终通过叠加110阶到150阶谐波，获得一个60as的孤立阿秒脉冲.同时，通过库仑势和激光场的相互作用势以及时频分布图解释了其中的物理机制.     

On a hidden symmetry of quantum harmonic oscillators

We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal kinematical invariance group on the standard solutions. In addition, the phase space oscillations of the electron position and linear momentum probability distributions are computer animated and some possible applications are briefly discussed. A visualization of the Heisenberg uncertainty principle is presented.     

Stuffed Tridymite Structures: Synthesis,Structure, Second Harmonic Generation,Optical, and Multiferroic Properties

The stuffed tridymite structure Ba(Zn/Co)_1−xSi_1−xM_2xO₄ (M=Al³⁺ and Fe³⁺) is explored for the possible multiferroic behavior and to develop new inorganic colored materials. The compounds were synthesized by employing conventional solid-state chemistry methods in the temperature range 1100–1175 °C for 24 h. The powder X-ray diffraction (PXRD) and Rietveld refinement studies indicate that the compounds stabilize in the P63 space group (no. 173). The refinement results were also rationalized by employing Raman spectroscopic studies. The compounds were found to be second harmonic generation (SHG) active and show weak ferroelectric behavior. The co-substitution of Co²⁺ and Fe³⁺ in the structure gives rise to a weak ferromagnetic behavior to the compound, BaCo_0.75Si_0.75Fe_0.5O₄, making it a multiferroic material. The optical studies on the prepared compounds exhibited blue color (Co²⁺ in T_d geometry), purple color (Ni²⁺ in T_d geometry), and simultaneous substitution of Co²⁺ and Fe³⁺ gives rise to blue-green color owing to metal-to-metal charge transfer (MMCT) effect.     

从机械能守恒的角度推导单摆简谐振动的周期

本文给出了利用基本的物理原理结合高等数学公式的方法推导单摆做简谐运动的周期公式,可以简明扼要地理解单摆简谐运动的过程.