论文标题
在存在增量功能电位的情况下，应用于谐波振荡器的变异方法
The variational method applied to the harmonic oscillator in presence of a delta function potential
论文作者
论文摘要
具有位于中央的三角洲功能电位的谐波振荡器的问题可以在一个维度上精确解决，在一个维度上，本征函数表示为HERMITE多项式的叠加或一般而言的汇合超测量功能。精确获得的本征函数很难可视化，因此很难获得更多的见解，可以尝试使用明确且简单地表达的模型波函数。在这里，我们采用变分方法来验证一个可以使用这种试验波函数接近确切基态特征值的近距离。我们获得了基态能量的估计值，这些估计值与排斥和有吸引力的三角洲电势的早期近似结果相比更接近确切值。
The problem of the harmonic oscillator with a centrally located delta function potential can be exactly solved in one dimension where the eigenfunctions are expressed as superpositions of the Hermite polynomials or as confluent hypergeometric functions in general. The eigenfunctions obtained exactly are difficult to visualise and hence to gain more insight, one can attempt using model wave functions which are explicitly and simply expressed. Here we apply the variational method to verify how close one can approach the exact ground state eigenvalues using such trial wave functions. We obtain the estimates of the ground state energies which are closer to the exact values in comparison to earlier approximate results for both the repulsive and attractive delta potentials.
