  In this paper, we study the Lagrangian F-stability and Hamiltonian
F-stability of Lagrangian self-shrinkers. We prove a characterization theorem
for the Hamiltonian F-stability of $n$-dimensional complete Lagrangian
self-shrinkers without boundary, with polynomial volume growth and with the
second fundamental form satisfying the condition that there exist constants
$C_0>0$ and $\varepsilon<\frac{1}{16n}$ such that $|A|^2\leq C_0+\varepsilon
|x|^2$. We characterize the Hamiltonian F-stablity by the eigenvalues and
eigenspaces of the drifted Laplacian.
