Constructive inversion of energy trajectories in quantum mechanics
Hall, Richard L.
arXiv, 9812058 / Harvested from arXiv
Text on arXiv
We suppose that the ground-state eigenvalue E = F(v) of the Schroedinger Hamiltonian H = -\Delta + vf(x) in one dimension is known for all values of the coupling v > 0. The potential shape f(x) is assumed to be symmetric, bounded below, and monotone increasing for x > 0. A fast algorithm is devised which allows the potential shape f(x) to be reconstructed from the energy trajectory F(v). Three examples are discussed in detail: a shifted power-potential, the exponential potential, and the sech-squared potential are each reconstructed from their known exact energy trajectories.
Publié le : 1998-12-18
Classification:  Quantum Physics,  Mathematical Physics 
@article{9812058,
     author = {Hall, Richard L.},
     title = {Constructive inversion of energy trajectories in quantum mechanics},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9812058}
}

Hall, Richard L. Constructive inversion of energy trajectories in quantum mechanics. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9812058/