An accurate finite difference method for the numerical solution of the Schrödinger equation

✍ Scribed by T.E. Simos

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 665 KB
• Volume: 91
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(98)00014-4

✦ Synopsis

An accurate finite difference approach for computing eigenvalues of Schr6dinger equations is developed in this paper.

We investigate two cases: (i) the specific case in which the potential V(x) is an even function with respect to x. It is assumed, also, that the wave functions tend to zero for x --~ =l=cx~. We investigate the well-known potential of the onedimensional anharmonic oscillator, the symmetric double-well potential, the Razavy potential and the doubly anharmonic oscillator potential. (ii) The general case for positive and negative eigenvalues and for the well-known cases of the Morse potential and Woods-Saxon or optical potential. Numerical and theoretical results show that this new approach is more efficient than previously derived methods.