Abstract
The q-boson algebra is defined as an associative algebra with generators and relations. Some examples are given, and then the q-boson algebra is extended such that the roots of the ‘diagonal generators’ are also defined. It is shown that a family of transformations exist mapping one set of standard generators of the q-boson algebra to another set of standard generators. Using such a transformation, one obtains expressions for q-bosons for which the kth q-boson state is expressed in terms of a q-Hermite polynomial p k (x; q) which reduces to the ordinary Hermite polynomial of degree k when q=1.
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