原子核振动与转动模型(Ⅰ)推转玻尔─莫特逊哈密顿量和偶偶核正常转动谱分析

从推转壳模型出发,导出了转动频率未量子化的集体振动-转动哈密顿量,称为推转玻尔-莫特逊哈密顿量(CBMH).引入合理的集体运动位势,由CBMH可以得到解析形式的转动谱公式.应用这一振动-转动模型,对偶偶变形核的正常转动能谱进行了分析,取得了满意的结果.     

原子核的U(6/20)超对称性及其Spin(6)极限

一、引言相互作用玻色子近似(IBA)模型成功地描写了某些偶偶核的性质。IBA模型有三种极限对称性:1)U(5)极限,相当于几何振动核,2)U(3)极限,相当于一种特殊的对称转动核,3)O(6)极限,相当于γ——非稳转动核。在这三种极限对称性下,可以求出IBA哈密顿量的解析解,而三种极限之间的中间结构可用数值计算来求解。近几年来,许多人用相同方法致力于研究奇核的性质,例如美国Drexel组在1983年9月苏州核集体激发态国际会议上就I(6/20)超对称性曾作过报告。相互作用玻色子-费米子近似(IBFA)模型可以求解奇质量核。这时哈密顿量为     

三体耦合摆量子系统的精确波函数

利用不变本征算符法研究了三体耦合摆量子系统的简正频率及其对应的简正坐标与共轭动量,并对系统的哈密顿量进行了退耦合,得到了系统的明显的简正频率解析解.推导出在坐标表象中系统的精确波函数的解析解.但是,不变本征算符法对于计算系统哈密顿量中包含力学量的3次方及3次方以上的项时非常复杂.     

原子核振动与转动模型（Ⅰ）推转玻尔─莫特逊哈密顿量和偶偶核正常转动谱分析

从推转壳模型出发，导出了转动频率未量子化的集体振动－转动哈密顿量，称为推转玻尔－莫特逊哈密顿量（ＣＢＭＨ）．引入合理的集体运动位势，由ＣＢＭＨ可以得到解析形式的转动谱公式．应用这一振动－转动模型，对偶偶变形核的正常转动能谱进行了分析，取得了满意的结果．     

相对论性非球谐振子势场中的赝自旋对称性

求解了非球谐振子势场中1/2自旋粒子满足的Dirac方程,Dirac哈密顿量包含有标量非球谐振子势S(r)和矢量非球谐振子势V(r).在Σ(r)=S(r)+V(r)=0和Δ(r)=V(r)-S(r)=0的条件下,解析地得到了Dirac旋量波函数的束缚态解和能谱方程,结果表明非球谐振子势 关键词： 非球谐振子势 Dirac方程 赝自旋对称性 束缚态     

锂原子能量的近似解

本文用屏蔽库仑势模型将锂原子的哈密顿量加以简化，然后用微扰法求解了锂原子一系列能级值，计算简洁，结果也与实验值符合得很好。     

具有在位势的一维双原子链中杂质引起的对称局域模

对具有在位势且含杂质的一维双原子链的晶格振动方程组进行求解,得到了局域振动的解析解,给出了在位势对局域振动影响的基本特征,并简要讨论了对称局域模的存在形式.     

类Quesne环状球谐振子势场中的赝自旋对称性

提出了一种新的类Quesne环状球谐振子势,应用二分量方法求解1/2-自旋粒子满足的Dirac方程, Dirac哈密顿量由标量和矢量类Quesne环状球谐振子势构成.在Σ=S(r)+V(r)=0的条件下,得到了Dirac旋量波函数下分量的束缚态解和能谱方程, 显示出类Quesne环状球谐振子势场中的赝自旋对称性.讨论了束缚态波函数和能谱方程的有关性质. 关键词： 类Quesne环状球谐振子势 Dirac方程 赝自旋对称性 束缚态     

具有在位势的一维双原子链中杂质引起的局域振动

对具有在位势且含杂质的一维双原子链的晶格振动方程组进行求解,得到了局域振动的解析解, 给出了在位势对局域振动影响的基本特征,并简要讨论了局域模的存在形式.     

具有Eckart势的Schrdinger方程的任意l波解析解

使用完全量子化规则计算了具有离心项的Eckart势,根据动量积分∫xBxAk(x)dx-∫x0Bx0Ak0(x)dx=nπ和Greene-Aldrich近似化条件,得到了系统的任意l波Schrdinger方程的解析解.讨论了:(1)基态和激发态下,势能范围参数λ和势阱深度η对具有不同角动量量子数的能量本征值的影响;(2)径向量子数n和角动量量子数l与能量本征值的关系.     

Study of Bohr–Mottelson with minimal length effect for Q-deformed modified Eckart potential and Bohr–Mottelson with Q-deformed quantum for three-dimensional harmonic oscillator potential

Bohr–Mottelson Hamiltonian on the γ-rigid regime for Q-deformed modified Eckart and three-dimensional harmonic oscillator potentials in the β-collective shape variable was investigated in the presence of minimal length formalism and Q-deformed of the radial momentum part. By introducing new wave function and using the Q-deformed potential concept in Bohr–Mottelson Hamiltonian in the minimal length formalism, the un-normalized wave function and energy spectra equation were obtained by using the hypergeometric method. Meanwhile, the Bohr–Mottelson Hamiltonian in the presence of the quadratic spatial deformation to the momentum in collective shape variable was investigated using transformation of a new variable such as the Schrodinger-like equation with shape invariant potential. The energy equation and un-normalized wave function were obtained using the hypergeometric method. The results showed that the Bohr–Mottelson equations with different energy potentials and different deformation forms in the radial momentum reduced to the similar Schrodinger-like equation with the modified Poschl–Teller potential.     

New exact Schrödinger-equation solutions based on finite-dimensional matrices

New exactly solvable models are found. The exact solutions pertain to low-lying states and are connected with the solution of the eigenvalue problem for three and five-diagonal matrices of special form. The solution can be described by introducing an effective spin Hamiltonian that is non-Hermitian in general but has real eigenvalues. The potentials obtained go over in various limiting cases into the Mathieu, Eckart, Peschl-Teller potential and into the effective potentials for anisotropic paramagnets.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 17–23, January, 1990.     

On the solution of the number-projected Hartree-Fock-Bogolyubov equations

The numerical solution of the recently formulated number-projected Hartree-Fock-Bogolyubov (HFB) equations is studied in an exactly solvable cranked-deformed shell-model Hamiltonian. It is found that the solution of these number-projected equations involves similar numerical effort as that of bare HFB. We consider that this is significant progress in the mean-field studies of quantum many-body systems. The results of the projected calculations are shown to be in almost complete agreement with the exact solutions of the model Hamiltonian. The phase transition obtained in the HFB theory as a function of the rotational frequency is shown to be smeared out with the projection.     

Validity of the two-determinantal deformed Hartree-Fock approximation

The two-fold degeneracy of the deformed Hartree-Fock (HF) solutions in thes-d shell suggests the use of a two-determinantal intrinsic state. The validity of this two-determinantal variational method is established in the case of the exactly solvable Lipkin Hamiltonian, for which the usual HF solution is known to be 2 fold degenerate. The approximation of using a two-determinantal intrinsic state turns out to be an exceedingly good one and in general as the particle number and the strength of the interaction increase, the exact solution is rapidly approached. The states of positive (negative) parity which are obtained by projection from the intrinsic two-determinantal state are found to reproduce the exact ground (first excited) state with a high accuracy.     

Molecular symmetry and motions of the Eckart frame

Motions of the Eckart frame, as defined in terms of the Eckart vector by Louck and Galbraith (4), are calculated for molecules belonging to several point groups. Differential changes in the associated Gram matrix are treated as perturbations. Explicit equations are developed for the motion of the Eckart frame in the special case where the matrix of the Eckart vectors (the F matrix) is diagonal.     

An exactly solvable model for the large polaron

We present an exactly diagonalizable model Hamiltonian for the large polaron derived by analyzing the variational ansatz by Haga-Larsen (HL) for the Fröhlich Hamiltonian. The lowest energy eigenvalue of the model Hamiltonian for fixed wave numbers reproduces the energy of the variational ansatz by Haga-Larsen and is, therefore, an upper bound with respect to the corresponding energy eigenvalue of the Fröhlich Hamiltonian. This is valid for any momentum which is proven by extending the Haga-Larsen approach. Furthermore, since all integrations can be performed analytically, the model Hamiltonian is easily tractable. The energy eigenvalue spectrum of the model Hamiltonian is studied below and above the phonon-emission threshold. The quality of the model Hamiltonian is determined by the variational ansatz of Haga and Larsen. Incorporating an improved energy-momentum relation, a generalized model Hamiltonian is derived possessing a larger validity range with respect to the coupling strength. Furthermore, a second exactly diagonalizable model Hamiltonian based on improved Wigner-Brillouin perturbation theory due to Warmenbol, Peeters, and Devreese (WPD) is presented. It is briefly demonstrated that one is able to construct all mentioned model Hamiltonians also in the 2D polaron problem. In contrast to the 3D case, where the HL-type model Hamiltonian possesses the higher quality for any momentum, in the 2D case, it works well only for small momenta. For large momenta, only the WPD-type model Hamiltonian describes the energy-momentum relation correctly. We demonstrate the usefulness of the model Hamiltonian concept by exactly calculating the one-electron Green’s function for all mentioned model Hamiltonians and comment why significant advantages of the model Hamilton concept for the treating of low-dimensional systems (planar semiconducting quantum-well structures) can be expected.     

E0 transitional density for nuclei between spherical and deformed shapes

The Generator Coordinate Method (GCM) is used to construct the effective nuclear density operator suitable for calculations of E0 transitional densities with collective eigenfunctions of the phenomenological Bohr Hamiltonian. For example, the 0⁺ _gs \( \rightarrow\) 0⁺ ₂ transitional density is calculated for the shape-phase transitional nucleus ¹⁵⁰Nd using the eigenfunctions of the approximate X(5) solution of the Bohr Hamiltonian.     

A new method for solving the two-center problem with realistic potentials

A method has been proposed for the solution of the two-center problem with realistic potentials. It consists of two steps: first, we make a separable approximation to the single-particle potentials, and then the two-center problem with these separable potentials is solved exactly. The only approximations are introduced at the first stage, and in a well controllable way. As an example, we have calculated the single-particle energies and wave functions in the field of two ¹⁶O-like Woods-Saxon potentials as functions of their distance R.     

Schrödinger equation for a particle on a curved surface in an electric and magnetic field

We derive the Schr?dinger equation for a spinless charged particle constrained to move on a curved surface in the presence of an electric and magnetic field. The particle is confined on the surface using a thin-layer procedure, which gives rise to the well-known geometric potential. The electric and magnetic fields are included via the four potential. We find that there is no coupling between the fields and the surface curvature and that, with a proper choice of the gauge, the surface and transverse dynamics are exactly separable. Finally, we derive an analytic form of the Hamiltonian for spherical, cylindrical, and toroidal surfaces.     

Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators

We construct a time-dependent double well potential as an exact spectral equivalent to the explicitly time-dependent negative quartic oscillator with a time-dependent mass term. Defining the unstable anharmonic oscillator Hamiltonian on a contour in the lower-half complex plane, the resulting time-dependent non-Hermitian Hamiltonian is first mapped by an exact solution of the time-dependent Dyson equation to a time-dependent Hermitian Hamiltonian defined on the real axis. When unitary transformed, scaled and Fourier transformed we obtain a time-dependent double well potential bounded from below. All transformations are carried out non-perturbatively so that all Hamiltonians in this process are spectrally exactly equivalent in the sense that they have identical instantaneous energy eigenvalue spectra.