When: Mar 25 2014
Standard introductory quantum mechanics course places emphasis on solving the time-independent Schrödinger equations. This talk will introduce algebraic methods for several quantum systems. Such methods are not only elegant but also powerful: one of the advantages is that we can employ a computer algebra system (e.g. Maple or Mathematica) to obtain solutions recursively. Time permitting, I'll discuss how Lie algebras, after the Norwegian mathematician Sophus Lie, make differential equations encountered in quantum mechanics more tractable. If I still have time, I'll mention the applications of Lie groups in nuclear and particle physics. Historical background will be reviewed, and Einstein's pioneer contribution to quantum theory will be presented as exercises from Precalculus to Calculus 3 levels.