# Bound State Wave Functions through the Quantum Hamilton - Jacobi Formalism

Source: [Bound State Wave Functions through the Quantum Hamilton - Jacobi Formalism](<https://www.sota2.com/research/paper/68fa25ee2c2a3760193b5145>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T11:03:46.663Z

Authors: S. Sree Ranjani, K. G. Geojo, A. K. Kapoor, P. K. Panigrahi

Published: 2002-11-26T07:58:20.000Z

## Abstract

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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/quant-ph/0211168>)

[PDF](<https://arxiv.org/pdf/quant-ph/0211168.pdf>)