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29 March 2024
 
  » arxiv » 1211.5236

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Solving for three-dimensional central potentials using matrix mechanics
B. A. Jugdutt ; F. Marsiglio ;
Date 22 Nov 2012
AbstractMatrix mechanics is an important component of an undergraduate education in quantum mechanics. Unfortunately it is generally taught only in the abstract, with real implementations relegated to more advanced degrees, and usually in the context of many-body physics. In this paper we present several examples of the use of matrix mechanics to solve for a number of three dimensional problems involving central forces. These include examples with which the student is familiar, such as the Coulomb interaction -- in this case we obtain excellent agreement with exact analytical methods, -- along with other interesting ’non-solvable’ examples, such as the Yukawa potential. Much less mathematical expertise is required for these methods, while some minimal familiarity with the usage of numerical diagonalization software is necessary.
Source arXiv, 1211.5236
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