New Semiclassical and Numerical Approaches to Locate Zeros of Wave Functions

A new semiclassical method is presented for evaluating zeros of wave functions. In this method, locating zeros of the wave functions of Schrodinger equation is converted to finding roots of a polynomial. The coefficients of this polynomial are evaluated using WKB and semi quantum action variable methods. For certain potentials WKB expressions for moments are obtained exactly. Almost explicit formulae for moments are obtained for the potential V(x)=x^N. Examples are given to illustrate both methods. Using semi quantum action variable method, complex zeros of the wave functions of the PT symmetric complex system V(x)=x^4 iAx are obtained. These zeros exhibit complex version of in terlacing.     

Letter: Hierarchy and Wave Functions in a Simple Quantum Cosmology

In a simple quantum cosmological model involving eleven dimensional space-time, an extended holographic conjecture suggests the nuclear force must be about forty orders of magnitude stronger than gravity. An interpretation of the wave function of the universe in this model is also proposed.     

Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).     

整数自旋粒子的方程和波函数

从高自旋态的Bargmann-Wigner方程出发,建立了整数自旋粒子的运动方程,通过求解方程得到了一套整数自旋粒子波函数,并建立了等效Largrange形式.     

Pilot Wave Steerage: A Mechanism and Test

An intuitive, generic, physical model, or conceptual paradigm for pilot wave steerage of particle beams based on Stochastic Electrodynamics is presented. The utility of this model for understanding the Pauli Exclusion Principle is briefly considered, and a possible experimental verification for the underlying concepts is proposed.     

A New Approach to Solve Nonlinear Wave Equations

From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this new approach, and more shock wave solutions or solitary wave solutions can be got under their limit conditions.     

Semiclassical Asymptotics of the Aharonov‐Bohm Interference Process

We systematically derive the semiclassical limit of a charged particle's motion in the presence of an infinitely long and infinitesimally thin solenoid carrying magnetic flux. Our limit establishes the connection of the particle's quantum mechanical canonical angular momentum to the latter's classical counterpart. A picture of Aharonov‐Bohm interference of two half‐waves acquiring Dirac's magnetic phase when passing on either side of the solenoid naturally emerges from the quantum propagator. The resulting interference pattern is fully determined by the ratio of the angular part of Hamilton's principal function to Planck's constant, and the wave interference smoothes out discontinuities in the semiclassical propagator which is recovered in the limit when the above ratio diverges. We discuss the relation of our results to the whirling‐wave representation of the exact propagator, and to previous approaches on the system's asymptotics.     

精确简洁解析的原子组态相互作用波函数的计算

使用广义Laguerre类型轨道,在组态相互作用框架内,发展并完善了一套精确、简洁、解析的原子(离子)波函数从头计算的Fortran程序,计算原子中电子的结构.通过对指定能态能量求其最小值实现对波函数节点位置和空间范围的优化,从而求出最优波函数.作为例子,计算了⁵G态下的Ti的能量最小值和优化波函数.     

具有奇异夸克系统的重子波函数

在重子波函数中考虑了s夸克与u,d夸克质量的差别,构造了把坐标空间与味空间联合成SU(3)_rf的SU(3)_rf×SU(2)_s×SU(3)_c群分类夸克间全反对称的重子波函数.与不考虑s夸克与u,d夸克质量差的SU(n)_r×SU(3)_f×SU(2)_s×SU(3)_c群分类的波函数作了比较,它们的相互作用能量矩阵元有明显的差别.     

整数自旋协变波函数

对高自旋态的Bargmann-Wigner方程的解进行了改造,给出了一套系统地构造高自旋态(整数自旋)协变波函数的新方法.利用这种方法,分别构造了任意整数自旋粒子的协变波函数.     

创立量子力学的睿智才思(续2)——纪念矩阵力学和波动力学诞生80～81周年

1922年前后玻尔-索末菲的旧量子论在原子结构理论上取得辉煌成就的同时，它的致命弱点也开始暴露出来．反常塞曼效应是其一，原子光谱的多重线结构是其二，更不要说氢分子离子H2^＋问题了．一时多少杰出的物理学家为这些问题绞尽脑汁，设计了各种物理模型，提出一些“代用（德文Er-satz）”理论，诸如海森伯和泡利的Zwang之类，到头来还只得愁眉以对，一筹莫展．无怪乎海森伯把反常塞曼效应叫做“光谱项的动物学和塞曼植物学（Term Zoology and Zeeman Botany）”，意即在这个领域里物理学家只能像生物学家那样记录现象和描绘事实，提不出像样的理论．到1925年下半年，人们手里有了矩阵力学，问题是否可以解决了呢？万事俱备，只欠“东风”，那就是“自旋”．     

Two-Variable Hermite Function as Quantum Entanglement of Harmonic Oscillator＇s Wave Functions

We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S（γ）Hm,n （μa1^＋, μa2^＋│00〉, which is the minimum uncertainty state for sum squeezing, in （ η│representation is calculated.     

渐变折射率介质中标准矢量波函数的构成

研究了在渐变折射率介质中构成标准矢量波函数的必要条件。研究结果表明在渐变折射率介质中构成标准矢量波函数除了仍需遵循Morse-Feshbach判据外，领示矢量仅能选取与折射率变化方向一致的那根坐标轴的单位矢量。     

等离子体非相对论性平均原子模型中类氢波函数

详述等离子体中非相对论性平均原子模型的诸方程,给出整个方程系统的求解步骤、数值技巧以及程序设计的具体细节.将变分法和试验势法得到的半解析结果与完全数值解以及略有差异的模型得到的数值解进行比较,指出该模型及其算法的优点和不足.     

Transitions to the Continuum: Three Different Approaches

We present three different derivations of the transition probabilities to the continuum. It is shown that calculations, performed as a direct application of the postulates of orthodox quantum mechanics (OQM), do not yield results consistent with experiments. Traditional treatments are summarized and criticized. The relation of the transitions to the continuum with the traditional quantum measurement problem is pointed out; we sum up and comment some contributions concerning this issue. It is shown that an approach based on the notion of spontaneous projections yields expressions of the transition probabilities similar to those obtained in the traditional way and new predictions which could be submitted to experimental tests.     

Propagation of General Wave Packets in Some Classical and Quantum Systems

In quantum mechanics the center of a wave packet is precisely defined as the center of probability. The center-of-probability velocity describes the entire motion of the wave packet. In classical physics there is no precise counterpart to the center-of-probability velocity of quantum mechanics, in spite of the fact that there exist in the literature at least eight different velocities for the electromagnetic wave. We propose a center-of-energy velocity to describe the entire motion of general wave packets in classical physical systems. It is a measurable quantity, and is well defined for both continuous and discrete systems. For electromagnetic wave packets it is a generalization of the velocity of energy transport. General wave packets in several classical systems are studied and the center-of-energy velocity is calculated and expressed in terms of the dispersion relation and the Fourier coefficients. These systems include string subject to an external force, monatomic chain and diatomic chain in one dimension, and classical Heisenberg model in one dimension. In most cases the center-of-energy velocity reduces to the group velocity for quasi-monochromatic wave packets. Thus it also appears to be the generalization of the group velocity. Wave packets of the relativistic Dirac equation are discussed briefly.     

Elliptic Equation and New Solutions to Nonlinear Wave Equations

The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on.     

Photon Wave Mechanics: A De Broglie-Bohm Approach

We compare the de Broglie-Bohm theory for non-relativistic, scalar matter particles with the Majorana-Römer theory of electrodynamics, pointing out the impressive common peculiarities and the role of the spin in both theories. A novel insight into photon wave mechanics is envisaged.     

Quantum equilibrium and the origin of absolute uncertainty

The quantum formalism is a measurement formalism-a phenomenological formalism describing certain macroscopic regularities. We argue that it can be regarded, and best be understood, as arising from Bohmian mechanics, which is what emerges from Schrödinger's equation for a system of particles when we merely insist that particles means particles. While distinctly non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles in motion, a motion choreographed by the wave function. We find that a Bohmian universe, though deterministic, evolves in such a manner that anappearance of randomness emerges, precisely as described by the quantum formalism and given, for example, by = ¦¦ ². A crucial ingredient in our analysis of the origin of this randomness is the notion of the effective wave function of a subsystem, a notion of interest in its own right and of relevance to any discussion of quantum theory. When the quantum formalism is regarded as arising in this way, the paradoxes and perplexities so often associated with (nonrelativistic) quantum theory simply evaporate.This paper is dedicated to the memory of J. S. Bell.