What is it about?

In this work, we show how one can determine wavefunctions in spherically symmetric problems by first determining the translation operator for radial problems and then using it to determine the wavefunctions for the Coulomb problems in 2 and 3 dimensions.

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Why is it important?

This allows one to compute the wavefunctions for radial problems using a representation-independent methodology. Such an approach is preferred than approaches that focus on working in one specific coordinate system


Readers interested in quantum mechanics pedagogy will find this work interesting as the existence of translation operators for radial problems has been ignored for so many years. Those interested in how one formulates quantum mechanics in a representation-independent fashion will also be interested by this work.

James Freericks
Georgetown University

Read the Original

This page is a summary of: Converting translation operators into plane polar and spherical coordinates and their use in determining quantum-mechanical wavefunctions in a representation-independent fashion, Journal of Mathematical Physics, July 2021, American Institute of Physics,
DOI: 10.1063/5.0021013.
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