A quantum anharmonic oscillator is defined by the Hamiltonian ${\cal H}=-\frac{ {\rm d^{2}}}{{\rm d}x^{2}} + V(x)$, where the potential is given by$V(x) = \sum_{i=1}^{m} c_{i} x^{2i}$ with $c_{m}>0$. Using the Sinc collocationmethod combined with the double exponential transformation, we develop a methodto efficiently compute highly accurate approximations of energy eigenvalues foranharmonic oscillators. Convergence properties of the proposed method arepresented. Using the principle of minimal sensitivity, we introduce analternate expression for the mesh size for the Sinc collocation method whichimproves considerably the accuracy in computing eigenvalues for potentials withmultiple wells. We apply our method to a number of potentials including potentials withmultiple wells. The numerical results section clearly illustrates the highefficiency and accuracy of the proposed method. All our codes are written usingthe programming language Julia and are available upon request.
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机译：量子非谐振荡器由哈密顿量$ {\ cal H} =-\ frac {{\ rm d ^ {2}}} {{\ rm d} x ^ {2}} + V（x）$定义，其中势由$ V（x）= \ sum_ {i = 1} ^ {m} c_ {i} x ^ {2i} $给出，其中$ c_ {m}> 0 $。使用Sinc搭配方法与双指数变换相结合，我们开发了一种方法，可以有效地计算非谐振荡器的能量特征值的高精度近似值。提出了该方法的收敛性。使用最小灵敏度原理，我们为Sinc配点方法引入了网格大小的替代表达式，这大大提高了计算具有多个孔的势的特征值的准确性。我们将我们的方法应用于许多潜力，包括多口潜力。数值结果部分清楚地说明了该方法的高效性和准确性。我们所有的代码都是使用Julia语言编写的，可应要求提供。
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