Solving the anharmonic oscillator: tuning the boundary condition
Solving the anharmonic oscillator: tuning the boundary condition
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DOI：
10.1088/1751-8113/40/33/020
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发表时间：
2007-03
期刊：
影响因子：
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通讯作者：
David S. Leonard;P. Mansfield
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文献类型：
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作者：
David S. Leonard;P. Mansfield
我们概述了一种非常有效的方法来产生具有x2M势的量子非谐振子的解。我们用一个自由参数来求解薛定谔方程，然后通过产生波函数在x上的幂级数展开式并应用改进的Borel恢复技术来获得大的x行为，然后调整这个参数以给出正确的边界条件。这一过程使我们能够计算出任意精度的能量本征值。即使用适度的计算能力，也能达到高度的精度。我们的技术扩展到所有级别的激发，并给出了双势垒振子的正确解，即使它们是由非微扰效应主导的。
We outline a remarkably efficient method for generating solutions to quantum anharmonic oscillators with an x2M potential. We solve the Schrödinger equation in terms of a free parameter which is then tuned to give the correct boundary condition by generating a power series expansion of the wavefunction in x and applying a modified Borel resummation technique to obtain the large x behaviour. The process allows us to calculate energy eigenvalues to an arbitrary level of accuracy. High degrees of precision are achieved even with modest computing power. Our technique extends to all levels of excitation and produces the correct solution to the double well oscillators even though they are dominated by non-perturbative effects.