New WKB method in supersymmetry quantum mechanics

In this paper, we combine the perturbation method in supersymmetric quantum mechanics with the WKB method to restudy an angular equation coming from the wave equations for a Schwarzschild black hole with a straight string passing through it. This angular equation serves as a naive model for our investigation of the combination of supersym- metric quantum mechanics and the WKB method, and will provide valuable insight for our further study of the WKB approximation in real problems, like the one in spheroidal equations, etc.     

Analytic solutions of the ground and excited states of the spin-weighted spheroidal equation in the case of s=2

By using the super-symmetric quantum mechanics (SUSYQM) method, this paper obtains the analytical solutions for the spin-weighted spheroidal wave equation in the case of s = 2. Based on the derived W 0 to W 4 the general form for the n-th-order super-potential is summarized and is proved correct by mathematical induction. Hence the ground eigenvalue problem is completely solved. Particularly, the novel solutions of the excited state are investigated according to the shape-invariance property.     

Low frequency asymptotics for the spin-weighted spheroidal equation in the case of s=1/2

The spin-weighted spheroidal equation in the case of s=1/2 is thoroughly studied by using the perturbation method from the supersymmetric quantum mechanics.The first-five terms of the superpotential in the series of parameter β are given.The general form for the n-th term of the superpotential is also obtained,which could also be derived from the previous terms W k,k < n.From these results,it is easy to obtain the ground eigenfunction of the equation.Furthermore,the shape-invariance property in the series of parameter β is investigated and is proven to be kept.This nice property guarantees that the excited eigenfunctions in the series form can be obtained from the ground eigenfunction by using the method from the supersymmetric quantum mechanics.We show the perturbation method in supersymmetric quantum mechanics could completely solve the spin-weight spheroidal wave equations in the series form of the small parameter β.     

Rediscussion of the Stability Problem of the Schwarzschild Black Hole

We use the Kruskal time coordinate T to define the initial time. By this way, the stability study naturally becomes the one connected with the two regions, i.e. the white-hole-connected region and the black-hole-connected region. The union of the two regions covers the Schwarzschild space-time （r ≥ 2m）. We also obtain the very reasonable conclusion： the white-hole-connected region is unstable and the black-hole-connected region is stable. If we take the instability with caution and seriousness, it is not unreasonable to regard that the Schwarzschild black hole might be unstable to some extent.     

How to Define the Equality of Durations in Measurement of Time

We develop the research on measurement of time worked by Poincarh, Einstein, Landau and other researchers. Based on the convention that the velocity of light is isotropic and is a constant in empty spacetime, we not only answer the question about the definition of the synchronization of rate of clocks located at different places, but also find the solution to the issue of how to define the equality of two durations in measurement of time.     

Ground eigenvalue and eigenfunction of a spin-weighted spheroidal wave equation in low frequencies

Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics.Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency.The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.     

A New Model For the Double Well Potential

A new model for the double well potential is presented. In the new potential, the exchanging rate could be easily calculated by the perturbation method in supersymmetric quantum mechanics. It gives good results whether the barrier is high or sallow. The new model has many merits and may be used in the double well problem.     

一类类光测地线的加速度

类光测地线γ0(λ)与二维类空超曲面φ正交，λ为其仿射参量.假如在类光测地线γ0(λ)上存在一点r(r=γ0(λr))共轭于类空超曲面φ，则对于γ0(λ)上任一点q(q=γ0(λq))满足λq＞λr，一定能把γ0连续变形成一条从φ到q的类时曲线.当产生类时曲线的变分矢量场不是类光测地线上的广义Jacobi场时，这些类时曲线在趋于类光测地线时，它们的固有加速度趋于无穷大. 关键词： 类光测地线 共轭点 变分     

Proper Accelerations of Time-Like Curves near a Null Geodesic

It is well known that when given a null geodesic γ0(λ) with a point r in (p,q) conjugate to p along γ0(λ), there will be a variation of γ0(λ) which can give a time-like curve from p to q. Here we prove that the time-like curves coming from the above-mentioned variation (with the second derivative β2≠0) have a proper acceleration A= √A^αAα which approaches infinity as the time-like curve approaches the null geodesic. Because the curve obtained from variation of the null geodesic must be everywhere time-like, we also discuss the constraint of the ‘acceleration’ B0^α of the variation vector field on the null geodesic γ0(λ). The acceleration B0^α of the variation vector field Z^α on the null geodesic γ0(λ) cannot be zero.     

Evolution of entanglement between qubits ultra-strongly coupling to a quantum oscillator

We investigate the dynamics of two qubits coupled with a quantum oscillator by using the adiabatic approximation method. We take account of the interaction between the qubits and show how the entanglement is affected by the interaction parameter. The most interesting result is that we can prolong the entanglement time or improve the entanglement degree by using an appropriate interaction parameter. As the generation and preservation of entanglement of qubits are crucial for quantum information processing, our research will be useful.