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In this paper, we continue the study of $T\bar{T}$ deformation in $d=1$quantum mechanical systems and propose possible analogues of $J\bar{T}$deformation and deformation by a general linear combination of $T\bar{T}$ and$J\bar{T}$ in quantum mechanics. We construct flow equations for the partitionfunctions of the deformed theory, the solutions to which yields the deformedpartition functions as integral of the undeformed partition function weightedby some kernels. The kernel formula turns out to be very useful in studying thedeformed two-point functions and analyzing the thermodynamics of the deformedtheory. Finally, we show that a non-perturbative UV completion of the deformedtheory is given by minimally coupling the undeformed theory to worldlinegravity and $U(1)$ gauge theory.

$T\bar{T}$ and $J\bar{T}$ Deformations in Quantum Mechanics