Table 1 Relation between the effective potential \(U_{\mathrm {eff}}\) and effective energy \(E_{\mathrm {eff}}\), indicating the four situations corresponding to different kinds of wavefunction solutions; notably, quasi-bound states exist in situation (2).
From: Quasi-bound states in an NPN-type nanometer-scale graphene quantum dot under a magnetic field
Situation | Solution of the wavefunction | |
|---|---|---|
(1) | \(E^2>\big(\frac{m}{R}+\frac{eBR}{2}\big)^2\) | Plane wave solutions |
(2) | \(2eBm<E^2\le \big(\frac{m}{R}+\frac{eBR}{2}\big)^2\) | Quasi-bound state solutions |
(3) | \(2EV_{0}-V_{0}^2+\big(\frac{m}{R}+\frac{eBR}{2}\big)^2<E^2\le 2eBm\) | Bound state solutions |
(4) | \(E^2<2EV_{0}-V_{0}^2+\big(\frac{m}{R}+\frac{eBR}{2}\big)^2\) | No solution |
