几种具有特殊性质的一维势函数谱的量子Hamilton-Jacobi解
Quantum Hamilton - Jacobi soluton for spectra of several one dimensional potentials with special properties
摘要：
本文将量子Hamilton - Jacobi（QHJ）方法用于（i）在不同的势参数范围内具有不同谱的势，（ii）精确可解（ES）周期势，（iii）拟精确可解（QES）周期势和（iv）PT对称势（ES和QES）。QHJ形式提供了一种简单而优雅的方法来获得束缚态和带边本征值和本征函数。为此目的，一个简单的猜想上的奇异性的对数导数的波函数在复平面上，并用于在一个直接向前的方式，以获得所需的结果。
英文摘要：
In this thesis the quantum Hamilton - Jacobi (QHJ) formalism is used for (i) potentials which exhibit different spectra for different ranges of the potential parameters, (ii) exactly solvable (ES) periodic potentials (iii) quasi - exactly solvable (QES) periodic potentials and (iv) the PT symmetric potentials (ES and QES). The QHJ formalism provides a simple and elegant method to obtain the bound state and the band edge eigenvalues and the eigenfunctions. For this purpose, a simple conjecture on the singularities of the logarithmic derivative of the wave function in the complex plane is made and used in a straight forward fashion to obtain the desired results.
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