The Quantum Nanowire Detector · AI Generator #GEN-EBDB070B
Physics · quantum-mechanics
Problem
A quantum nanowire detector consists of electrons confined in a one-dimensional infinite square well of width L=2.0nm. When a photon is absorbed, an electron transitions from the ground state to the first excited state. The detector is designed to be sensitive to infrared radiation at wavelength λ=12.4μm.
However, due to manufacturing imperfections, the nanowire contains a small perturbation: a delta-function potential V(x)=−V0δ(x−L/2) at the center of the well, where V0=2.5eV⋅nm.
(a) Calculate the energy of the photon that the unperturbed detector is designed to detect.
(b) Find the first-order energy correction to the ground state due to the delta-function perturbation.
(c) Determine how much the transition energy (ground state to first excited state) changes due to this perturbation, and calculate the new wavelength to which the detector is most sensitive.