  We present the analysis of mathematical structure of SU(2) group,
specifically the commutation relation between raising and lowering operators of
the Morse oscillator. The relationship between the commutator of operators and
other parameters of Morse oscillator is investigated. We show that the
mathematical structure of operators which depends on the parameters of Morse
oscillator may change our conventional expectation. The parameter space of
Morse oscillator is visualized to scrutinize the mathematical relations that
are related to the Morse oscillator. This parameter space is the space of
possible parameter values that depend on the depth of the Morse potential well
and other parameters. The algorithm that we present is also applicable to other
quantum systems with certain modifications.
