双曲平面上有磁场和实直线上有Morse势的波核
Wave kernels with magnetic field on the hyperbolic plane and with the Morse potential on the real line
摘要：
本文给出了圆盘上和双曲平面上半平面模型上带有磁场的修正薛定谔算子的波动方程的显式解。通过一维傅里叶变换，证明了上半平面模型上带磁场的修正薛定谔算符与$\R$上带双原子分子Morse势的薛定谔算符之间的关系.利用这个关系，我们给出了$\R$上双原子分子Morse势的薛定谔算子的波核在二元合流超几何函数$Φ_1$下的显式表示.
英文摘要：
In this article we give explicit solutions for the wave equations associated to the modified Schrödinger operators with magnetic field on the disc and the upper half plane models of the hyperbolic plane. We show that the modified Schrödinger operator with magnetic field on the upper half plane model and the Schrödinger operator with diatomic molecular Morse potential on $\R$ are related by means of one-dimensional Fourier transform. Using this relation we give the explicit forms of the wave kernels associated to the Schrödinger operator with the diatomic molecular Morse potential on $\R$ in terms of the two variables confluent hypergeometric function $Φ_1$.
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