  In this article, we present a new quantum Painlev\'e II Lax pair which
explicitly involves the Planck constant $ \hbar $ and an arbitrary field
variable $v$ so these two objects make this new pair different from
Flaschka-Newell Painlev\'e II Lax pair and that pair appears as particular case
of our's pair which consolidates the Painlev\'e II equation from quantum
mechanical point of view. It is shown that the compatibility of quantum
Painlev\'e II Lax pair simultaneously yields a quantum Painlev\'e II equation
and a quantum commutation relation between field variable $v $ and independent
variable $z$. We manifest that with the different choices of arbitrary field
variable system reduces to its classical version, matrix Painlev\'e II equation
and derivative matrix Painlev\'e II equation. Further, we construct the gauge
equivalence of quantum Painlev\'e II Lax pair whose compatibility condition
gives rise to quantum p34 equation that involves $\hbar $ with power $+1$ which
makes our system more quantized as compared to the existed one that carries
$\hbar $ with power $+2$.
