| Abstract: | In Part 1 of this two-part article we have spelt out, in some detail, the link between symmetries and conservation principles
in the Lagrangian and Hamiltonian formulations of classical mechanics (CM). In this second part, we turn our attention to
the corresponding question in quantum mechanics (QM). The generalization we embark upon will proceed in two directions: from
the classical formulation to the quantum mechanical one, and from a single (infinitesimal) symmetry to a multi-dimensional
Lie group of symmetries. Of course, we always have some definite physical system in mind. We also assume that the reader is
familiar with the elements of quantum mechanics at the level of a standard first course on the subject. Operators will be
denoted with an overhead caret, e.g., $
\hat A,\hat G,\hat U
$
\hat A,\hat G,\hat U
, etc., while $
\hat A,\hat B] = \hat A\hat B - \hat B\hat A
$
\hat A,\hat B] = \hat A\hat B - \hat B\hat A
is the commutator of $
\hat A
$
\hat A
and $
\hat B
$
\hat B
. |
