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Closed-form solutions for the Schrödinger wave equation with non-solvable potentials: A perturbation approach
Open Physics ( IF 1.9 ) Pub Date : 2021-01-01 , DOI: 10.1515/phys-2021-0028
Haifa Ibrahim Alrebdi 1 , Thabit Barakat 2
Affiliation  

To obtain closed-form solutions for the radial Schrödinger wave equation with non-solvable potential models, we use a simple, easy, and fast perturbation technique within the framework of the asymptotic iteration method (PAIM). We will show how the PAIM can be applied directly to find the analytical coefficients in the perturbation series, without using the base eigenfunctions of the unperturbed problem. As an example, the vector Coulomb ( ∼ 1 / r ) \left( \sim 1\hspace{0.1em}\text{/}\hspace{0.1em}r) and the harmonic oscillator ( ∼ r 2 ) \left( \sim {r}^{2}) plus linear ( ∼ r ) \left( \sim r) scalar potential parts implemented with their counterpart spin-dependent terms are chosen to investigate the meson sectors including charm and beauty quarks. This approach is applicable in the same form to both the ground state and the excited bound states and can be easily applied to other strongly non-solvable potential problems. The procedure of this method and its results will provide a valuable hint for investigating tetraquark configuration.

中文翻译:

具有不可解势的Schrödinger波动方程的闭式解:一种摄动方法

为了获得具有不可解势模型的径向Schrödinger波动方程的闭式解,我们在渐近迭代法(PAIM)的框架内使用了一种简单,便捷和快速的摄动技术。我们将展示如何在不使用无扰动问题的基本特征函数的情况下,将PAIM直接应用于扰动序列的解析系数。例如,向量库仑(〜1 / r)\ left(\ sim 1 \ hspace {0.1em} \ text {/} \ hspace {0.1em} r)和谐波振荡器(〜r 2)\ left(选择\ sim {r} ^ {2})加上线性(〜r)\ left(\ sim r)标量潜在部分及其对应的自旋相关项,以研究介子部分,包括魅力夸克和美丽夸克。该方法可以以相同的形式应用于基态和激发束缚态,并且可以轻松地应用于其他不可解决的潜在问题。该方法的程序及其结果将为研究四夸克构型提供有价值的提示。
更新日期:2021-01-01
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