Quantum Newtonian cosmology and the biconfluent Heun functions

Heun functions describing bosons and fermions on Melvin's spacetime

Employing a pseudo-orthonormal coordinate-free approach, the solutions to the Klein--Gordon and Dirac equations for particles in Melvin spacetime are derived in terms of Heun's biconfluent functions.

量子谐振子中的模拟黑洞弦

Analogue black string in a quantum harmonic oscillator

本文以双合流赫恩函数精确求解无电荷静态黑洞弦背景下的克莱因-戈尔登方程，发现负质量粒子具有复能量（暗示准正规模），并构造了可模拟该系统的简单量子谐振子。

Comment on "Comment on linear confinement of a scalar particle in a Gödel-type space-time"

We show that from an appropriate manipulation of the biconfluent Heun differential equation can obtain the correct expression for the energy eigenvalues for the Klein-Gordon equation without potential in the background of Som-Raychaudhuri space-time with a cosmic string as a case particular ($k_{L}=0$) of [Vitória et al. Eur. Phys. J. C (2018) 78:44], in opposition what was stated in a recent paper published in this journal [F. Ahmed, Eur. Phys. J. C (2019) 79:682].

5维施瓦西-唐赫利尼时空：约化合流超几何方程的类MST形式主义

5d Schwarzschild-Tangherlini spacetime: MST-like formalism for a Reduced Confluent Heun Equation

研究五维施瓦西-唐赫利尼时空，在探针极限下计算非束缚测地线散射角等，还研究无质量标量微扰动力学，扩展MST形式主义，计算重整化角动量参数并分析圆轨道能量通量，获2.5PN阶后牛顿结果。

重整化后闵可夫斯基和后牛顿引力波形展开

Resumming Post-Minkowskian and Post-Newtonian gravitational waveform expansions

本文推导了在软极限下重整化史瓦西几何中粒子轨迹引力波形的后闵可夫斯基/后牛顿修正无穷级数的公式，计算了圆轨道30PN阶波形和能流并与文献对比，其结果基于Heun方程解的新颖超几何表示并证明了Heun连接公式。

Some exact results on quantum Newtonian cosmology

We obtain the wave functions associated to the quantum Newtonian universe with a cosmological constant which is described by the Schrödinger equation and discuss some aspects of its dynamics for all forms of energy density, namely, matter, radiation, vacuum, dark energy, and quintessence. These wave functions of the quantum Newtonian universe are obtained in terms of the Heun's functions and the respective energy levels are shown. We use these solutions to investigate the expansion of the universe and found that the asymptotic behavior for the scale factor is $R \sim \mbox{e}^{t}$ for whatever…