Quantum correction in exact quantization rules
By Zhong-Qi Ma, Bo-wei Xu. 2005
175 citations recorded by the source corpus.
An exact quantization rule for the Schrodinger equation is presented. In the exact quantization rule, in addition to Nπ, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the quantum correction is an invariant, independent of the number of nodes in the wave function. In those systems, the energy levels of all the bound states can be easily calculated from the exact quantization rule and the solution for the ground state, which can be obtained by solving the Riccati equation. With this new method, we re-calculate the energy levels for the one-dimensional systems with a finite square well, with the Morse potential, with the symmetric and asymmetric Rosen-Morse potentials, and with the first and the second Poschl-Teller potentials, for the harmonic oscillators both in one dimension and in three dimensions, and for the hydrogen atom.
Subfields: Atomic and Molecular Physics, and Optics, Physical and Theoretical Chemistry
View Paper: https://www.semanticscholar.org/paper/2d0430085712af1894c8fbd50908ca148f4482a3
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
In Physical and Theoretical Chemistry
Citations in the corpus
- Hidden pseudospin and spin symmetries and their origins in atomic nuclei (2014, methodology): “of potential ∆(r), by using the Nikiforov-Uvarov (NU) method [279], the supersymmetric quantum mechanics [252], the asymptotic it erat on method [280], the exact quantization rule [281], and so on.”