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A previous paper of the author developed a general method for producingexplicit central elements of quantized Lie algebras using Lusztig's innerproduct. This method had previously been applied for the type $C_2$, $D_3$ and$D_4$ Lie algebras. The current paper repeats the calculation for the type$B_2$ Lie algebra, which is actually isomorphic to the $C_2$ Lie algebra. Theexplicit expression for the corresponding quantum Hamiltonian is computed.

An explicit central element of $\mathcal{U}_q(\mathfrak{so}_5)$ and its corresponding quantum Hamiltonian