The evolution of bound states in quantum wires under potential modulation

We calculate the bound state energies in various quantum wires under potential modulation, including crossed, T-shaped and L-shaped quantum wires. It is found that the bound state energy rapidly increases with the potential height in the lower potential region while it slowly approaches a limit in the higher potential region. A fit formula that describes the dependence of the bound state energy and the potential height is obtained. Based on the formula and the contour plots of electron probability density, the relation and evolution of bound states in different quantum wire systems are shown. We also find that the bound state in a quantum dot, in some potential-modulation region, turns into a quasibound state with finite lifetime.