Lessons for Students and Educators in Developing Quantum Mechanical Wave Functions Using Slater Determinant and Sum-of-Permutations Methodologies

Abstract Students who are engaged in understanding physical and chemical phenomena and/or designing devices that involve various atomic and molecular systems benefit from an understanding of general concepts that underlie quantum chemistry and quantum mechanics. Wave functions are one of the most basic and important concepts for understanding quantum chemistry, but many students in quantum mechanics courses struggle to write and interpret these functions correctly. This Tutorial presents novel instructional content related to the creation of multiparticle wave functions for multielectron systems using both the Slater determinant and the older sum-of-permutations equations. Late 20th century and early 21st century textbooks typically utilize the Slater determinant for describing multiparticle wave functions. Sum-of-permutations equations that are used in some early and mid-20th century texts and papers can be ambiguous and confusing when compared to the Slater determinant. Herein, we clarify the ambiguity present in the sum-of-permutations equations and provide guidance through examples and lessons to demonstrate that these older equations are equivalent to the newer Slater determinant form. By bridging the gap between past and current approaches for creating multiparticle wave functions, this Tutorial elucidates multidisciplinary teaching and learning opportunities in the area of quantum chemistry and quantum mechanics.