具有正则奇点的薛定谔方程的TBA方程
TBA equations for the Schrödinger equation with a regular singularity
摘要：
本文导出了具有任意多项式势和正则奇异项（单极点和双极点）的薛定谔方程的热力学贝特安伯（TBA）方程。TBA方程提供了ODE/IM对应的非平凡推广，并且也给出了精确WKB方法中Riemann-Hilbert问题的解。我们详细研究了TBA方程的线性和谐振子势连同逆项和离心项。作为一个应用，我们还计算了数值的Voros频谱这些潜在的玻尔索末菲量子化条件。
英文摘要：
We derive the Thermodynamic Bethe Ansatz (TBA) equations for the Schrödinger equation with an arbitrary polynomial potential and a regular singular (simple and double pole) term. The TBA equations provide a non-trivial generalization of the ODE/IM correspondence and also give a solution for the Riemann-Hilbert problem in the exact WKB method. We study the TBA equations in detail for the linear and the harmonic oscillator potentials together with inverse and centrifugal terms. As an application, we also compute numerically the Voros spectrum for these potentials using the Bohr-Sommerfeld quantization condition.
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