Scanning tunneling spectrum of electrons confined in a rectangular quantum corral

We obtained the scanning tunneling spectrum (STS) of an electron confined in a rectangular quantum corral by considering the electron to be in a quasi-stationary state. Because of non-hermiticity of the Hamiltonian, the electron has a complex eigenenergy. The imaginary part gives the peak width coming mainly from the electron tunneling through a corral barrier. Our STS is consistent with the experimental spectrum that had been measured for electrons confined in a rectangular quantum corral. We obtained peak widths against energy levels and components of the STS which are constructed with quasi-stationary eigenstates. It is shown that normalization of a wavefunction by considering its time evolution is decisive in obtaining the proper STS. Moreover, we specified the position dependence of STS in relation to the image of the surface local density of states.