  Usually in quantum mechanics the Heisenberg algebra is generated by operators
of position and momentum. The algebra is then represented on an Hilbert space
of square integrable functions. Alternatively one generates the Heisenberg
algebra by the raising and lowering operators. It is then natural to represent
it on the Bargmann Fock space of holomorphic functions. In the following I show
that the Bargmann Fock construction can also be done in the quantum group
symmetric case. This leads to a 'q- deformed quantum mechanics' in which the
basic concepts, Hilbert space of states and unitarity of time evolution, are
preserved.
