论文标题
通用四分之一振荡器的不常见精确能量
Uncommonly accurate energies for the general quartic oscillator
论文作者
论文摘要
对电势能水平的渐近分析的最新进展在$ 10^{ - 34} $的特征值总和中产生相对误差，但是在数值上以这种准确性求解了很少的非平凡潜力。我们使用数百个振荡器状态的基础来解决超过此准确性的一般四分之一潜能（任意线性组合的$ x^2 $和$ x^4 $）。我们列出了9个此类电位的最低20个特征值。我们为纯四分之一振荡器的水平确认已知的渐近扩展，并在渐近扩张中提取接下来的2个术语。我们提供分析公式，以扩展多达3个偶数状态。我们确认各种能量成分的病毒定理具有相似的精度。还给出了六振荡器水平。这些基准结果对于化学物理及其他几个领域的近似值的极端测试应该很有用。
Recent advances in the asymptotic analysis of energy levels of potentials produce relative errors in eigenvalue sums of order $10^{-34}$, but few non-trivial potentials have been solved numerically to such accuracy. We solve the general quartic potential (arbitrary linear combination of $x^2$ and $x^4$ ) beyond this level of accuracy using a basis of several hundred oscillator states. We list the lowest 20 eigenvalues for 9 such potentials. We confirm the known asymptotic expansion for the levels of the pure quartic oscillator, and extract the next 2 terms in the asymptotic expansion. We give analytic formulas for expansion in up to 3 even basis states. We confirm the virial theorem for the various energy components to similar accuracy. The sextic oscillator levels are also given. These benchmark results should be useful for extreme tests of approximations in several areas of chemical physics and beyond.
