# 2: Position and Momentum

So far, we have considered *general* dynamical variables represented by *general* linear operators acting in ket space. However, in classical mechanics, the most important dynamical variables are those involving position and momentum. Let us investigate the role of such variables in quantum mechanics. In classical mechanics, the position \(q\) and momentum \(p\) of some component of a dynamical system are represented as *real numbers* which, by definition, commute. In quantum mechanics, these quantities are represented as *non-commuting* linear Hermitian operators acting in a ket space that represents all of the possible states of the system. Our first task is to discover a quantum mechanical replacement for the classical result \(qp-pq = 0\).

### Contributors

- Richard Fitzpatrick (Professor of Physics, The University of Texas at Austin)