An Inversion Inequality for Potentials in Quantum Mechanics
Hall, Richard L.
arXiv, 9809019 / Harvested from arXiv
Text on arXiv
We suppose: (1) 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; and (2) that the potential shape can be expressed in the form f(x) = g(x^2), where g is monotone increasing and convex. The inversion inequality f(x) <= fbar(1/(4x^2)) is established, in which the `kinetic potential' fbar(s) is related to the energy function F(v) by the transformation: fbar(s) = F'(v), s = F(v) - vF'(v) As an example f is approximately reconstructed from the energy function F for the potential f(x) = x^2 + 1/(1+x^2).
Publié le : 1998-09-09
Classification:  Quantum Physics,  Mathematical Physics 
@article{9809019,
     author = {Hall, Richard L.},
     title = {An Inversion Inequality for Potentials in Quantum Mechanics},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9809019}
}

Hall, Richard L. An Inversion Inequality for Potentials in Quantum Mechanics. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9809019/