We consider the Mourre inequality for the following self-adjoint operator \( H=\Psi(-\Delta/2)+V$ acting on $L^2(\mathbb{R}^d) \), where \( \Psi: [0,\infty)\rightarrow\mathbb{R} \) is an increasing function, \( \Delta \) is the Laplacian and \( V: \mathbb{R}^d\rightarrow\mathbb{R} \) is an interaction potential. Mourre inequality immediately yields the discreteness and finite multiplicity of the eigenvalues. Moreover, the Mourre inequality together with the limiting absorption principle can be used to show absence of the singular continuous spectrum. In addition, Mourre inequality is also used for the proof of the minimal velocity estimate that plays an important role in scattering theory. In this talk, we report that Mourre inequality holds under a general \( \Psi \) and \( V \) by choosing the conjugate operator \( A=(p \cdot x + x \cdot p)/2 \) with \( p= - i \nabla \), and that the discreteness and finite multiplicity of the eigenvalues hold. This talk is a joint work with J. Lőrinczi (Alfred Rényi Institute) and I. Sasaki (Shinshu University).