𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Two-sided eigenvalue bounds for the spherically symmetric states of the Schrödinger equation

✍ Scribed by A. Zafer; H. Taşeli

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
874 KB
Volume
95
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

The eigenvalues of the radial Schr6dinger equation are calculated very accurately by obtaining exact upper and lower bounds. By truncating the usual unbounded domain [0,cx~) of the system to a finite interval of the form [0,g], two auxiliary eigenvalue problems are defined. It is then proved that the eigenvalues of the resulting confined systems provide upper and lower bounds converging monotonically to the true eigenvalues required. Moreover, each auxiliary eigenvalue problem gives rise to an orthonormal set involving Bessel functions. The matrix representation of the Hamiltonian is, therefore, derived by expanding the wave function into a Fourier-Bessel series. Numerical results for single-and doublewell polynomial oscillators as well as Gaussian type non-polynomial potentials illustrate that the eigenvalues can be calculated to an arbitrary accuracy, whenever the boundary parameter g is in the neighborhood of some critical value, denoted by Ecr.

📜 SIMILAR VOLUMES

Eigenvalue corrector for solving bound s
Eigenvalue corrector for solving bound states of multichannel Schrödinger equations
✍ M.L. Du 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 724 KB

An eigenvalue corrector is given for solving bound states in multichannel Schrodinger equations. Using the renonnalized Numerov method the multichannel equation is integrated from both left and right to the middle. The integrations define an approximate solution which is used to calculate the eigenv

Bound states of the coupled-channel Schr
Bound states of the coupled-channel Schrödinger equation: General eigenvalue function
✍ Khaled Fakhreddine; Hafez Kobeissi; Mahmoud Korek 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 165 KB 👁 1 views

The eigenvalue problem for a system of N coupled one-dimensional Schrodinger equations, arising in bound state in quantum mechanics, is considered. A canonical approach for the calculation of the energy eigenvalues of this system is presented. This method replaces the use of the wave functions by 2

Numerical solution of eigenvalues for th
Numerical solution of eigenvalues for the Schrödinger equation
✍ J.W. Neuberger; D.W. Noid 📂 Article 📅 1984 🏛 Elsevier Science 🌐 English ⚖ 267 KB

A method is proposed and tested for the quantum mechanical calculation of eigenvalues for a hamiltonian consisting of three coupled oscillators. The agreement of eisenvalues with a large variational calcularion is excellenr.