论文标题
库仑和谐波电位的电荷量化
Quantization of the charge in Coulomb plus harmonic potential
论文作者
论文摘要
我们考虑了两个模型，其中波动方程可以简化为有效的schrödinger方程，其电势包含谐波和库仑项，$ω^{2} r^{2} -a/r $。该方程将减少到双音量HEUN的方程式，我们发现电荷和能量必须量化并依赖于状态。我们还发现，要计算径向自由度的量子数是必要的两个量子数，并认为这是微分方程的一般特征，具有较高的奇异性，例如Heun方程。
We consider two models where the wave equation can be reduced to the effective Schrödinger equation whose potential contains both harmonic and the Coulomb terms, $ω^{2}r^{2}-a/r$. The equation reduces to the biconfluent Heun's equation, and we find that the charge as well as the energy must be quantized and state dependent. We also find that two quantum numbers are necessary to count radial degrees of freedom and suggest that this is a general feature of differential equation with higher singularity like the Heun's equation.
