Abstract
On a one-dimensional lattice with a geometric sequence spacing, the Hermitian conjugation of a (p,q)-derivative operator is discussed by means of (p,q)-integration. Then a (p,q)-deformation of both the Heisenberg algebra for the canonical coordinates and the Heisenberg–Weyl algebra for the harmonic oscillator is presented. It is shown that although in the algebraic aspect the (p,q)-deformation discussed here is identical with q-deformation given by Truong, the (p,q)-deformed Schrödinger picture is in fact different from the q-deformed one.
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