Resonance States and Non-Hermittian Quantum Mechanics: An Application to Nano-Tips
The resonance states or quasi-stationary states have been known from scattering theory of quantum systems. These states are like stationary states but with a finite lifetime after which they will not remain localized. They arise in various problems and we can consider them as the eigenfunctions of a non-Hermittian Hamiltonian. Using these states to describe the time evolution of the system can be of great advantage over the standard Hermitian formalism in some classes of problems. In addition to providing us with a better understanding of the physics of the system in consideration, it is sometimes the only possible way to computationally model the system. In my research, I am solving a simplified model for metallic nano-tips using these resonance states. In this talk, I will show the power of this formalism in attacking some problems including our simplified model, and then I briefly talk about the current state of my research.