Differentiability of degenerate electronic wave functions with respect to parametric variables

✍ Scribed by Li Yin; Osvaldo Goscinski

• Book ID: 104582783
• Publisher: John Wiley and Sons
• Year: 1990
• Tongue: English
• Weight: 436 KB
• Volume: 37
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560370305

✦ Synopsis

Abstract

The present paper is aimed at differentiability of electronic wave functions, with respect to parametric variables, in the presence of electronic degeneracy. An analysis is made of a wave function, constructed so that it has the largest domain of parameter space in which it is differentiable, with the help of Berry's formula for the geometric phase. In particular, the electronic wave functions, in presence of a double degeneracy in two‐ and three‐dimensional parameter spaces, are studied in detail. It was found that the three‐parameter‐dependent wave function is differentiable everywhere except along an axis starting from the degenerate point where it is discontinuous. The two‐parameter‐dependent wave function is differentiable everywhere except at the degenerate point where it is disocontinuous. These singularities are expected to have consequences on wave functions having parametric variables as arguments.