A numerical technique for solving Schrödinger's Equation in molecular electronic applications

A. J. Smith; A. R. Baghai-Wadji

doi:10.1117/12.814318

30 December 2008 A numerical technique for solving Schrödinger's Equation in molecular electronic applications

A. J. Smith, A. R. Baghai-Wadji

Proceedings Volume 7268, Smart Structures, Devices, and Systems IV; 72681Q (2008) https://doi.org/10.1117/12.814318
Event: SPIE Smart Materials, Nano- and Micro-Smart Systems, 2008, Melbourne, Australia

Abstract

For modelling molecular electronic and electrochemical boundary value problems (BVPs), we are faced with the solution of Schrodingers equation involving realistic models for potential energy functions. With the exception of a few canonical problems, there are currently no analytical methods available for obtaining closed-form solutions for the electron wavefunctions and their corresponding energy eigenvalues. One of the well-known techniques for obtaining approximate wavefunctions and energy states is the WKB approximation. The main drawbacks of the WKB method are the discontinuities at the so called turning points, where the total energy equals the potential energy and the restriction on exclusively solving for bound state solutions. To overcome these shortcomings, a novel accelerated numerical technique for solving time-independent Schrodingers equation is introduced, with applications to general potential functions. This method is based on the construction of an auxiliary BVP, which mimics significant features of the original BVP and possesses exact solutions. By construction, these solutions constitute a complete set of orthogonal problem-adapted analysing functions. This method provides numerical solutions with no discontinuities at the turning points.

Citation Download Citation

A. J. Smith and A. R. Baghai-Wadji "A numerical technique for solving Schrödinger's Equation in molecular electronic applications", Proc. SPIE 7268, Smart Structures, Devices, and Systems IV, 72681Q (30 December 2008); https://doi.org/10.1117/12.814318

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available