30 citations · 212 across the 33 of their papers we have counts for
33 papers
Perturbation-based Non-perturbative Method
Chang Liu, Wen-Du Li, Wu-Sheng Dai
This paper presents a nonperturbative method for solving eigenproblems. This method applies to almost all potentials and provides nonperturbative approximations for any energy leve…
Duality family of KdV equation
Xin Gu, Yuan-Yuan Liu, Wen-Du Li +1
It is revealed that there exist duality families of the KdV type equation. A duality family consists of an infinite number of generalized KdV (GKdV) equations. A duality transforma…
Renormalization of divergent moment in probability theory
Ping Zhang, Wen-Du Li, Wu-Sheng Dai
Some probability distributions have moments, and some do not. For example, the normal distribution has power moments of arbitrary order, but the Cauchy distribution does not have p…
Energy spectrum of interacting gas: cluster expansion method
Hao-Dan Li, Shi-Lin Li, Yu-Jie Chen +2
In this paper, we calculate the energy spectrum of interacting gases by converting the cluster expansion method in statistical mechanics into a method of solving energy eigenvalues…
Scattering approach for calculating one-loop effective action and vacuum energy
Yuan-Yuan Liu, Shi-Lin Li, Yu-Jie Chen +2
We propose an approach for calculating one-loop effective actions and vacuum energies in quantum field theory. Spectral functions are functions defined by the eigenvalues of an ope…
Constructing effective action for gravitational field by effective potential method
Shi-Lin Li, Yu-Jie Chen, Yu-Zhu Chen +2
The aim of this paper is to construct a quantum effective action for gravitational fields by the effective potential method in quantum field theory. The minimum of the quantum effe…
Eliminating oscillation in partial sum approximation of periodic function
Shi-Lin Li, Yuan-Yuan Liu, Wen-Du Li +1
If we cannot obtain all terms of a series, or if we cannot sum up a series, we have to turn to the partial sum approximation which approximate a function by the first several terms…
Quantum correction of gravitational constant
Yu-Jie Chen, Shi-Lin Li, Yu-Zhu Chen +2
We suggest a scheme for considering the quantum correction of the gravitational constant. In the model, the gravitational constant originates from a coupling of the gravitational f…
Exactly solvable Gross-Pitaevskii type equations
Yuan-Yuan Liu, Wen-Du Li, Wu-Sheng Dai
TWe suggest a method to construct exactly solvable Gross-Pitaevskii type equations, especially the variable-coefficient high-order Gross-Pitaevskii type equations. We show that the…
Bose-like few-fermion systems
Yu-Lin Zhao, Chi-Chun Zhou, Wen-Du Li +1
Dealing with a few-fermion system in the canonical ensemble, rather than in the grand canonical ensemble, shows that a few-fermion system with odd number fermions behaves different…
Duality family of scalar field
Wen-Du Li, Wu-Sheng Dai
We show that there exists a duality family of self-interacting massive scalar fields. The scalar field in a duality family are related by a duality transformation. Such a duality o…
A duality in classical and quantum mechanics: General results
Wen-Du Li, Wu-Sheng Dai
We reveal a duality in classical and quantum mechanics. Dual systems are related by duality transforms. All mechanical systems that are dual to each other form a duality family. In…
A duality of fields
Wen-Du Li, Wu-Sheng Dai
It is shown that there exists a duality among fields. If a field is dual to another field, the solution of the field can be obtained from the dual field by the duality transformati…
Probability Thermodynamics and Probability Quantum Field
Ping Zhang, Wen-Du Li, Tong Liu +1
We introduce probability thermodynamics and probability quantum fields. By probability we mean that there is an unknown operator, physical or nonphysical, whose eigenvalues obey a…
Scalar field in Reissner-Nordström spacetime: Bound state and scattering state
Shi-Lin Li, Yuan-Yuan Liu, Wen-Du Li +1
In this paper, we solve the massive scalar field in the Reissner-Nordström spacetime. The scalar field in the Reissner-Nordström spacetime has both bound states and scattering stat…
Geodesic dual spacetime
Wen-Du Li, Wu-Sheng Dai
A duality between spacetime manifolds, the geodesic duality, is introduced. Two manifolds are geodesic dual, if the transformation between their metrics is also the transformation…
Scalar scattering in Schwarzschild spacetime: Integral equation method
Wen-Du Li, Yu-Zhu Chen, Wu-Sheng Dai
An integral equation method for scalar scattering in Schwarzschild spacetime is constructed. The zeroth-order and first-order scattering phase shift is obtained.
Long-range potential scattering: Converting long-range potential to short-range potential by tortoise coordinate
Wen-Du Li, Wu-Sheng Dai
Inspired by general relativity, we suggest an approach for long-range potential scattering. In scattering theory, there is a general theory for short-range potential scattering, bu…
Quantum Newton duality
Wen-Du Li, Wu-Sheng Dai
Newton revealed an underlying duality relation between power potentials in classical mechanics. In this paper, we establish the quantum version of the Newton duality. The main aim…
Gravitational wave scattering theory without large-distance asymptotics
Wen-Du Li, Shi-Lin Li, Yu-Jie Chen +2
In conventional gravitational wave scattering theory, a large-distance asymptotic approximation is employed. In this approximation, the gravitational wave is approximated by its la…
Acoustic scattering theory without large-distance asymptotics
Chi-Chun Zhou, Wen-Du Li, Wu-Sheng Dai
In conventional acoustic scattering theory, a large-distance asymptotic approximation is employed. In this approximation, a far-field pattern, an asymptotic approximation of the ex…
A 1+5-dimensional gravitational-wave solution: curvature singularity and spacetime singularity
Yu-Zhu Chen, Wen-Du Li, Wu-Sheng Dai
We solve a -dimensional cylindrical gravitational-wave solution of the Einstein equation, in which there are two curvature singularities. Then we show that one of the curvatur…
Renormalization for singular-potential scattering
Wen-Du Li, Wu-Sheng Dai
In the calculation of quantum-mechanical singular-potential scattering, one encounters divergence. We suggest three renormalization schemes, dimensional renormalization, analytic c…
Scattering state and bound state of scalar field in Schwarzschild spacetime: Exact solution
Wen-Du Li, Yu-Zhu Chen, Wu-Sheng Dai
The main aim of this paper is twofold. (1) Exact solutions of a scalar field in the Schwarzschild spacetime are presented. The exact wave functions of scattering states and bound-s…