Supersymmetric ground state wave functions

The construction of explicit supersymmetric ground states is considered in a variety of quantum mechanical systems. For broad classes of supersymmetric hamiltonians it is not difficult to find closed-form zero-energy ground-state wave functions.     

He和类He离子基态能量与波函数的变分计算

在研究Pekeris模型的基础上,提出了一种包含坐标张弛系数的试探波函数,同时利用Matlab(或者Mathematica)语言,开发了一个运用变分法对三体问题进行计算的软件程序.在此基础上对He原子和类He离子的基态能量和解析波函数进行了变分计算,得到了比较理想的结果.这表明,采用Matlab或Mathematica设计的软件,在处理变分法问题时,在运算功能、数据的可靠性和准确度方面都是很具潜力的.     

Electromagnetic and weak constraints on the ground state wave functions of C and N

The nuclear wave functions of the A = 13 ground state isodoublet system are analysed by constraining them (within the 1p shell) to fit the best available electromagnetic and weak data. It is found that the wave functions are dominated by only two basis states of the possible five, with a greater degree of configuration mixing than that predicted by Cohen-Kurath. The use of these phenomenological wave functions to study ¹³C(γ, π⁻)¹³N_g.s. at low energies gives better agreement with data than using Cohen-Kurath wave functions but a factor of three enhancement still persists.     

Variational wave functions for the biexciton in polar semiconductors

Biexciton ground state energy has been calculated using several trial functions which possess proper symmetry, allow analytical evaluation of the energy matrix elements and include electron-electron and hole-hole correlations. Lattice polarization has been taken into account by means of the effective Hamiltonian with the potential being the sum of Coulomb, Yukawa and exponential terms. The average distances between the particles and the oscillator strengths of the exciton-biexciton conversion have been computed for the optimum trial function.     

On the F-center ground state wave function

We present a type of isotropic envelope for the F-center ground state wave function, suggested by ENDOR experimental data. We discuss it within a moment analysis of the experimental F-absorption spectrum.     

Variational methods for the ground state of liquid helium4

Assuming a Bijl-Jastrow-type wave function for the ground state of liquid He⁴, one can express the energy as a functional of the pair distribution functiong(r) when use is made of one of several “cluster approximations” known from the theory of classical fluids. The applicability of these approximations, and especially an integrodifferential equation forg(r) derived byAbe andHiroike, are discussed. It is shown that both the HNC and the PY approximations, when used consistently, yield the phonon behaviour of the liquid-structure factorS(k) for smallk. In the HNC approximation the energy as a function of density is calculated by a variational procedure. The velocity of sound following from \(\mathop {\lim }\limits_{k \to 0} \) S(k) is in good agreement with experiments and, at the equilibrium density, also with that calculated from the energy-versus-density curve. In the PY approximation a minimum of the energy expectation value does not exist without further restrictions on the trial wave function.     

Approximate formulae for the overlap integral of two harmonic oscillator wave functions

The use of second-order perturbation theory to derive approximate formulae for the overlap integral of two harmonic oscillator wave functions is discussed, and the results applied to the theory of intensity distributions in vibrational progressions in electronic spectra. For the vibrational progression m←0 an approximate formula is given which, when the vibrational frequencies of the initial and final states differ by less than 10%, reproduces to an accuracy of 1% or less the intensity profile calculated using the exact formulae for the overlap integrals.     

He原子非相对论基态能量的变分计算

本文指出了一种现象:当忽略原子核的运动时,He原子非相对论基态变分能量的计算值将会低于实验值.考虑对原子核运动的修正后,通过使用一个带松弛坐标参数k的变分波函数对He原子的非相对论基态能量进行了变分计算,得到比较满意的结果.此计算与变分原理一致.     

Variational path integral approach to the ground state energy of artificial atoms

Artificial atoms in different confinement potentials are studied using the Jensen–Feynman variational approach. The density and pair correlation function of an harmonic model with statistics are analytically calculated and used to find the variational ground state energy in two and three dimensions. The results are compared with the numerical calculations and a good correlation is found.     

Variational theory for the ground state and collective excitations of an elongated dipolar condensate

We develop a variational theory for a dipolar condensate in an elongated(cigar shaped)confinement potential. Our formulation provides an effective one-dimensional extended meanfield theory for the ground state and its collective excitations. We apply our theory to investigate the properties of rotons in the system comparing the variational treatment to a full numerical solution. We consider the effect of quantum fluctuations on the scattering length at which the roton excitation softens to zero energy.     

Exponential decay of bound state wave functions

The spatial decay properties of the wave functions of multiparticle systems are investigated. The particles interact through pair potentials in the classR+L . The bound states lie below the bottom of the continuous spectrum of the system. Exponential decay, in anL ² sense, is proven for these wave functions. The result is the best possible one which will cover every potential in this class.Based on a thesis submitted to Princeton University in partial fulfillment of the degree of Doctor of Philosophy.     

Variational wave functions in calculations of the forces of oscillators in atoms and ions

The present article discusses the quality of wave functions obtained within the framework of different variational methods. The advantages of the minimax method, which incorporates the ordinary variational method, are discussed. Using as an example the calculation of the force of oscillators, it is shown that a consistent set of complete wave functions determined within the framework of the minimax method yields better agreement with the force of oscillators calculated by means of the length and velocity methods than does the ordinary variational method. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 114–119, May, 1998.     

氩原子基态波函数和能量的解析计算

以第一性原理和变分原理为基础,给出了氩原子基态波函数的一种解析表达式,计算了基态氩原子(含类氩离子)的能量,导出了所涉及的所有积分的解析表达式.对氩原子,所得到的能量理论值与实验值的相对误差为0.22%.     

Detecting topological order in a ground state wave function

A large class of topological orders can be understood and classified using the string-net condensation picture. These topological orders can be characterized by a set of data (N, di, F(lmn)(ijk), delta(ijk). We describe a way to detect this kind of topological order using only the ground state wave function. The method involves computing a quantity called the "topological entropy" which directly measures the total quantum dimension D= Sum(id2i).     

The first order ground state wave functional for Yang-Mills

The ground state wave functional for pure SU(2) Yang-Mills in the temporal gauge is calculated to first order in the coupling constant. The standard formula for the perturbed wave function fails to give the correct form. The wave functional may be obtained by applying the Gauss law constraint.     

A single-parameter trial wave function for the mixed valence ground state

The mixed valence trial ground state suggested by Stevens and Brandow is reconsidered in the case of two electrons per atom. The wellknown difficulties due to nonorthogonality are resolved by expanding the trial state in an orthonormal basis. The expansion coefficients are determinants composed of Bloch phase factors, as in the Gutzwiller method. Studying first the limiting case of the Kaplan-Mahanti strongly localized ground state in the Brandow formalism, we derive rules for a simplified handling of the determinants; this opens the way to the more complicated weakly localized ground state. This is handled by expressing theN variational parameters of the Brandow formalism through a single one, the hybridization temperature . The ground state energy is a well-behaved function of the hybridization matrix elementV. The valence and the shift of the Fermi level are calculated to lowest order inV. The band occupation numbers follow a Fermi distribution at temperature V. We argue that the ground state is insulating, with thed-electrons localized into large Wannier-type orbitals centered on the respectivef-holes, as envisaged by Stevens.     

Electronic properties of quasi-one-dimensional compounds with a charge/spin-density wave ground state

First, a review of the general properties of the collective transport induced by the charge (CDW)/spin (SDW) density wave motion in quasi-one-dimensional conductors is presented. Then the three recent developments in this field are emphasized, namely: high spatial resolution x-ray study of the field-induced CDW deformations; quantum interference effects in magnetotransport of a sliding CDW through columnar defects; manifestation of disorder in the CDW/SDW ground state in thermodynamic properties at very low temperatures. Fiz. Tverd. Tela (St. Petersburg) 41, 759–763 (May 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Calculation of the wave functions of the ground and weakly excited states of helium II

The wave functions of the ground (Ψ₀) and the first excited (Ψ_k) states of He II in the second-order approximation, i.e., up to the first two corrections to the corresponding solutions for a weakly nonideal Bose gas, are determined by the collective variable method, which was proposed by Bogolyubov and Zubarev and developed in the studies by Yukhnovskii and Vakarchuk. The functions Ψ₀ and Ψ_k = ψ_kΨ₀ are determined as the eigenfunctions of the N-particle Schrödinger equation from a system of coupled equations for Ψ₀, Ψ_k, and the quasiparticle spectrum E(k) of helium II. The results consist in the following: (1) these equations are solved numerically for a higher order approximation compared with those investigated earlier (the first-order approximation), and (2) Ψ₀ and ψ_k are derived from a model potential of interaction between He⁴ atoms (rather than from the structure factor as earlier) in which the potential barrier is joined with the attractive potential found from experiment. The height V ₀ of the potential barrier is a free parameter. Except for V ₀, the model does not have any free parameters or functions. The calculated values of the structure factor, the ground-state energy E ₀, and the quasiparticle spectrum E(k) of He II are in agreement with the experimental values for V ₀ ≈ 100 K. The second-order correction to the logarithm of Ψ₀ significantly affects the value of E ₀ and provides the asymptotics E(k → 0) = ck, while the second-order correction to ψ_k slightly affects the E(k). The second-order corrections to Ψ₀ and ψ_k have a smaller effect on the results compared with the first-order corrections, whereby the theory is in agreement with experiment; therefore, one may assume that the truncated Ψ₀ and ψ_k well describe the microstructure of He II. Thus, the series for Ψ₀ and Ψ_k can be truncated in spite of the fact that the expansion parameter is not very small (～1/2).