用量子Hamilton - Jacobi公式计算束缚态波函数
Bound State Wave Functions through the Quantum Hamilton - Jacobi Formalism
摘要：
利用量子Hamilton-Jacobi形式，得到了一类精确可解势的束缚态波函数。它表明，利用奇异结构的量子动量函数，直到现在只用于获得束缚态能量，可以直接找到本征值和相应的本征函数。在通过一些可解的例子演示了这种方法的工作之后，我们考虑了哈密顿算子，它表现出超对称性的破缺和未破缺相。自然出现的本征谱和波函数，在两个不间断和代数非平凡的破碎阶段，证明了这种形式主义的效用。
英文摘要：
The bound state wave functions for a wide class of exactly solvable potentials are found utilizing the quantum Hamilton-Jacobi formalism. It is shown that, exploiting the singularity structure of the quantum momentum function, until now used only for obtaining the bound state energies, one can straightforwardly find both the eigenvalues and the corresponding eigenfunctions. After demonstrating the working of this approach through a number of solvable examples, we consider Hamiltonians, which exhibit broken and unbroken phases of supersymmetry. The natural emergence of the eigenspectra and the wave functions, in both the unbroken and the algebraically non-trivial broken phase, demonstrates the utility of this formalism.
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