Relations between low-lying quantum wave functions and solutions of the Hamilton-Jacobi equation

@article{Friedberg1999RelationsBL,
  title={Relations between low-lying quantum wave functions and solutions of the Hamilton-Jacobi equation},
  author={Richard Friedberg and Taek Dong Lee and Wen Qi Zhao},
  journal={Il Nuovo Cimento A (1971-1996)},
  year={1999},
  volume={112},
  pages={1195-1228}
}
SummaryWe discuss a new relation between the low-lying Schrödinger wave function of a particle in a one-dimensional potential V andthe solution of the corresponding Hamilton-Jacobi equation with —V as its potential. The functionV is ≥ 0, andcan have several minima (V = 0). We assume the problem to be characterized by a small anharmonicity parameterg-1 anda much smaller quantum tunneling parameter ɛ between these different minima. Expanding either the wave function or its energy as a formal… CONTINUE READING
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