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1.
In this paper, the analytical solutions of Schr¨odinger equation for Brownian motion in a double well potential are acquired by the homotopy analysis method and the Adomian decomposition method. Double well potential for Brownian motion is always used to obtain the solutions of Fokker–Planck equation known as the Klein–Kramers equation, which is suitable for separation and additive Hamiltonians. In essence, we could study the random motion of Brownian particles by solving Schr¨odinger equation. The analytical results obtained from the two different methods agree with each other well. The double well potential is affected by two parameters, which are analyzed and discussed in details with the aid of graphical illustrations. According to the final results, the shapes of the double well potential have significant influence on the probability density function. 相似文献
2.
With the Skyrme energy-density functional theory, the nucleus–nucleus potential is calculated and the potential energy surface is obtained with different effective forces for accurately estimating the formation cross sections of superheavy nuclei in massive fusion reactions. The width and height of the potential pocket are influenced by the Skyrme effective forces SkM, SkM*, SkP, SIII, Ska, and SLy4, which correspond to the different equations of state for the isospin symmetry nuclear matter. It is found that the nucleus–nucleus potential is associated with the collision orientation and Skyrme forces. A more repulsive nuclear potential is pronounced with increasing the incompressible modulus of nuclear matter, which hinders the formation of superheavy nuclei. The available data in the fusion-evaporation reaction of 48Ca+238U are nicely reproduced with the SkM* parameter by implementing the potential into the dinuclear system model. 相似文献
3.
We intend to realize the step-up and step-down operators of the potential V (x) = V1 e 2βx + V2 e βx. It is found that these operators satisfy the commutation relations for the SU(2) group. We find the eigenfunctions and the eigenvalues of the potential by using the Laplace transform approach to study the Lie algebra satisfied the ladder operators of the potential under consideration. Our results are similar to the ones obtained for the Morse potential (β → -β). 相似文献
4.
A Woods—Saxon potential is introduced to serve as initial conditions for an iterative solution of the exotic nuclei in relativistic mean field approach. Effects of parametrization of the Woods—Saxon potential on single particle orbits around the Fermi surface are investigated in 66Ca. A semi-parabolic curve of orbital radius appears when the width of the central potential changes. The pseduospin splitting is more sensitive to the potential width than to the depth and the diffuseness. The spin-orbit splitting is more sensitive to the potential depth than to the width and the diffuseness. 相似文献
5.
The Hellmann potential, which is a superposition of an attractive Coulomb potential -a/r and a Yukawa potential b e-δr/r, is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov-Uvarov (NU) method, we have obtained the approximate analytical solutions of the radial Schrödinger equation (SE) for the Hellmann potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented, which show good agreement with a numerical amplitude phase method and also those previously obtained by other methods. As a particular case, we find the energy levels of the pure Coulomb potential. 相似文献
6.
Bound states resulting from interaction of the non-relativistic particles with the multiparameter potential
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In this study, we present the analytical solutions of bound states for the Schrodinger equation with the multiparameter potential containing the different types of physical potentials via the asymptotic iteration method by applying the Pekeristype approximation to the centrifugal potential. For any n and l(states) quantum numbers, we derive the relation that gives the energy eigenvalues for the bound states numerically and the corresponding normalized eigenfunctions. We also plot some graphics in order to investigate effects of the multiparameter potential parameters on the energy eigenvalues.Furthermore, we compare our results with the ones obtained in previous works and it is seen that our numerical results are in good agreement with the literature. 相似文献
7.
B. Spagnolo A. Dubkov 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,50(1-2):299-303
The one-dimensional overdamped Brownian motion in a symmetric
periodic potential modulated by external time-reversible noise is
analyzed. The calculation of the effective diffusion coefficient
is reduced to the mean first passage time problem. We derive
general equations to calculate the effective diffusion coefficient
of Brownian particles moving in arbitrary supersymmetric potential
modulated by: (i) an external white Gaussian noise and (ii) a
Markovian dichotomous noise. For both cases the exact expressions
for the effective diffusion coefficient are derived. We obtain
acceleration of diffusion in comparison with the free diffusion
case for fast fluctuating potentials with arbitrary profile and
for sawtooth potential in case (ii). In this case the parameter
region where this effect can be observed is given. We obtain also
a finite net diffusion in the absence of thermal noise. For
rectangular potential the diffusion slows down, for all parameters
of noise and of potential, in comparison with the case when
particles diffuse freely. 相似文献
8.
A.A. Rajabi 《理论物理通讯》2007,48(1):151-158
An exact closed form of solution to the hyperradial Schrödinger equation is constructed for any general case
comprising any hypercentral power and inverse-power potential.
The hypercentral potential depends only on the hyperradius, which itself is a function of Jacobi relative
coordinates that are functions of particle positions
(r1,r2,…,
rN). This
article is mainly devoted to the dernonstrat of the fact that any
ψ of the form ψ=power series×
exp(polynomial)=[f(x)exp(g(x))]
is potentially a solution of the Schrödinger equation, where the polynomial g(x) is an ansatz depending on the interaction potential. 相似文献
9.
针对中点钳位型(NPC)三电平逆变器存在的直流侧中点电位不平衡问题,提出了一种基于模糊控制
的中点电位平衡策略。该策略重新定义了虚拟空间矢量,使虚拟小矢量不引起中点电位波动,并在虚拟中矢量中
引入了对中点电位不平衡有抑制作用的控制因子 Q。同时,设计了由模糊控制器 A 和 B 构成的组合模糊控制器,
该控制器能够依据中点电位偏移情况调整控制因子 Q,实现对中点电位的闭环控制。仿真和实验结果表明,采用
该策略的 NPC 型三电平逆变器中点电位不平衡问题能得到有效改善。 相似文献
10.
S Miraboutalebi 《中国物理 B》2016,25(10):100301-100301
We investigate an analytical solution for the Schr o¨dinger equation with a position-dependent mass distribution, with the Morse potential via Laplace transformations. We considered a mass function localized around the equilibrium position.The mass distribution depends on the energy spectrum of the state and the intrinsic parameters of the Morse potential. An exact bound state solution is obtained in the presence of this mass distribution. 相似文献
11.
This paper deals with the solutions of time independent Schrödinger wave equation for a two-dimensional PT-symmetric coupled quintic potential in its most general form. Employing wavefunction ansatz method, general analytic expressions for eigenvalues and eigenfunctions for first four states are obtained. Solutions of a particular case are also presented. 相似文献
12.
We investigate the Schrödinger equation for a particle with a nonuniform solitonic mass density. First, we discuss in extent the (nontrivial) position-dependent mass V(x)=0 case whose solutions are hypergeometric functions in tanh2x. Then, we consider an external hyperbolic-tangent potential. We show that the effective quantum mechanical problem is given by a Heun class equation and find analytically an eigenbasis for the space of solutions. We also compute the eigenstates for a potential of the form V(x)=V0 sinh2x. 相似文献
13.
The effect of confined one-gluon-exchange potential and instanton-induced interaction potential in the singlet(~1S_0) and triplet(~3S_1) channels for nucleon–nucleon interaction has been investigated in the framework of the relativistic harmonic model using the resonating group method in the adiabatic limit with the Born–Oppenheimer approximation. The contributions of the different components of the interaction potentials have been analyzed. 相似文献
14.
We study Bose-Einstein condensation in a linear trap with a dimple potential where we model dimple potentials by Dirac δ function. Attractive and repulsive dimple potentials are taken into account. This model allows simple, explicit numerical and analytical investigations of noninteracting gases. Thus, the Schrdinger equation is used instead of the Gross-Pitaevski equation. We calculate the atomic density, the chemical potential, the critical temperature and the condensate fraction. The role of the relative depth of the dimple potential with respect to the linear trap in large condensate formation at enhanced temperatures is clearly revealed. Moreover, we also present a semi-classical method for calculating various quantities such as entropy analytically. Moreover, we compare the results of this paper with the results of a previous paper in which the harmonic trap with a dimple potential in 1D is investigated. 相似文献
15.
16.
In the present work, we systematically investigate the proton radioactivity half-lives of spherical proton emitters adopting a generalized liquid drop model(GLDM) with 16 different proximity potentials, of which the proximity potential Prox.77-13 gives the closest results to the experimental data. Combined with the previous conclusion that the GLDM with proximity potential Prox.77-13 can also best describe α decay half-lives, which makes the model more uniform and consistent.Further, we use the proximity potential Prox.77-13 in GLDM to predict the proton radioactivity half-lives of 14 spherical proton emitters that are allowed energetically but not yet observed experimentally or specifically quantified. Finally, we research the Geiger-Nuttall law for proton radioactivity. The results reveal that the Geiger-Nuttall law can also be well used to study the proton radioactivity half-lives of isotopes with the same orbital angular momentum l. 相似文献
17.
In this paper, based on physics-informed neural networks (PINNs), a good deep learning neural network framework that can be used to effectively solve the nonlinear evolution partial differential equations (PDEs) and other types of nonlinear physical models, we study the nonlinear Schrödinger equation (NLSE) with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential, which is an important physical model in many fields of nonlinear physics. Firstly, we choose three different initial values and the same Dirichlet boundary conditions to solve the NLSE with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential via the PINN deep learning method, and the obtained results are compared with those derived by the traditional numerical methods. Then, we investigate the effects of two factors (optimization steps and activation functions) on the performance of the PINN deep learning method in the NLSE with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential. Ultimately, the data-driven coefficient discovery of the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential or the dispersion and nonlinear items of the NLSE with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential can be approximately ascertained by using the PINN deep learning method. Our results may be meaningful for further investigation of the nonlinear Schrödinger equation with the generalized ${ \mathcal P }{ \mathcal T }$-symmetric Scarf-II potential in the deep learning. 相似文献
18.
In contrast to Gaussian or Woods-Saxon potential a two-term four parameter nuclear Hulth′en type interaction is considered to describe the α-α, α-~3He and α-~3H systems. By exploiting the phase function method, scattering phase shifts are computed up to ELab = 100 MeV for the α-α system and ELab = 15 Me V for α-~3He and α-~3H systems.The S-wave phase shift δ_0 for the α-α system tends to 2π and δ_(3/2)-for the α-~3He system tends to π, in the limit of zero energy. Reasonable agreements in phase shifts with the standard data are obtained with this simple potential model except for the 5/2~- states of α-~3He and α-~3H systems. With an additional energy-dependent correction factor to our potential, a good agreement with experimental data is obtained for 5/2~- states. We have also compared our results with the convenient Born approximations. 相似文献
19.
We propose improved ring shaped like potential of the form, V(r,θ)=V(r)+(?2/2Mr2) [(βsin2θ +γcos2θ +λ)/sin θcosθ]2 and its exact solutions are presented via the Nikiforov-Uvarov method. The angle dependent part V(θ)=(?2/2Mr2) [(βsin2θ +γcos2θ +λ)/sin θcosθ]2, which is reported for the first time embodied the novel angle dependent (NAD) potential and harmonic novel angle dependent potential (HNAD) as special cases. We discuss in detail the effects of the improved ring shaped like potential on the radial parts of the spherical harmonic and Coulomb potentials. 相似文献
20.
Ituen B Okon Cecilia N Isonguyo Akaninyene D Antia Akpan N Ikot Oyebola O Popoola 《理论物理通讯》2020,72(6):65104-56
In this work, we determine the Fisher and Shannon entropies, the expectation values and the squeeze state for a noncentral inversely quadratic plus exponential Mie-type potential analytically.The proposed potential is solved under the Schr?dinger equation using a special Greene Aldrich approximation to the centrifugal term to obtain a normalised wave function within the framework of the Nikiforov–Uvarov method. Numerical results are obtained for different screening parameters:α?=?0.1, 0.12 and 0.13 for varying real constant parameter(B). The numerical solutions are obtained only for ground state. The numerical results of Fisher entropy both for position and momentum spaces are in good agreement with existing literature. The normalisation constant, wave function, and probability density plots are carried out using a well designed Mathematica algorithm.The Fourier transform of position space entropy gives the momentum space entropy. 相似文献