arXiv quant-ph/03021572003-02-20quant-ph

准精确可解双阱势近似格式的发展

Development of an approximation scheme for quasi-exactly solvable double-well potentials

R. Atre, P. K. Panigrahi

备注：: 11 pages, 3 figures, Revtex format

摘要：

我们利用最近开发的方法，不仅获得确切已知的本征态和本征值的一些准精确可解的哈密顿量，但也构造了一个收敛的近似计划定位这些水平，不服从分析处理。上述方法得到了波函数关于相应能量的展开式，这一事实使人们能够将能量作为变分参数来处理，它可以有效地用于本征态的识别。这对于基态已知且本征态有界的拟精确可解系统特别有用。通过获得典型双阱势的低位激发态来说明该方法的有效性，其中传统技术不是很可靠。我们的方法产生的近似本征函数和本征值，其精度可以提高到任何所需的水平，在一个控制的方式。将本文的结果与独立的数值方法的结果进行比较，发现我们的近似解中的前几项足以得到激发态本征值，精确到小数点后第三位。

英文摘要：

We make use of a recently developed method to, not only obtain the exactly known eigenstates and eigenvalues of a number of quasi-exactly solvable Hamiltonians, but also construct a convergent approximation scheme for locating those levels, not amenable to analytical treatments. The fact that, the above method yields an expansion of the wave functions in terms of corresponding energies, enables one to treat energy as a variational parameter, which can be effectively used for the identification of the eigenstates. It is particularly useful for the quasi-exactly solvable systems, where the ground state is known and a number of eigenstates are bounded, both below and above. The efficacy of the procedure is illustrated by obtaining, the low-lying excited states of a prototypical double-well potential, where the conventional techniques are not very reliable. Our approach yields the approximate eigenfunctions and eigenvalues, whose accuracy can be improved to any desired level, in a controlled manner. Comparing the present results with those of an independent numerical method, it was found that, the first few terms in our approximate solutions are enough to yield the excited state eigenvalues, accurate upto the third place of the decimal.

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摘要：

英文摘要：

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