  In this note, we study the potential algebra for several models arising out
of quantum mechanics with generalized uncertainty principle. We first show that
the eigenvalue equation corresponding to the momentum-space Hamiltonian
\[H=-(1+\beta p^{2})\frac{d}{dp}(1+\beta
p^{2})\frac{d}{dp}+g(g-1)\beta^{2}p^{2}-g\beta,\] which is associated with some
one-dimensional models with minimal length uncertainty, can be solved by the
unitary representations of the Lie algebra $\mathfrak{su}(2)$ if
$g\in\{\tfrac{1}{2},1,\tfrac{3}{2},2,\cdots\}$. We then apply this result to
spectral problems for the non-relativistic harmonic oscillator as well as the
relativistic Dirac oscillator in the presence of a minimal length and show that
these problems can be solved solely in terms of $\mathfrak{su}(2)$.
