Let $ \Delta =\frac{\partial^2}{\partial x_1^2}+\frac{\partial^2}{\partial x_2^2}+\frac{\partial^2}{\partial x_3^2}$ be the Laplacian on $ \mathbb{R}^3$ . Consider an operator $ H$ on complex valued functions on $ \mathbb{R}^3$ $ $ H\psi=\Delta\psi(x) +i\sum_{p=1}^3A_p(x)\frac{\partial \psi(x)}{\partial x_p} +B(x)\psi(x),$ $ where $ A_i,B$ are smooth real valued functions.

I am looking for a precise result of the following approximate form: (1) if $ A_i$ and $ B$ are ‘small’ then the discrete spectrum of $ H$ is non-positive. (2) If $ A_i,B$ are ‘large’ then the discrete spectrum of $ H$ contains necessarily a positive element.