Problem 1. Consider the following 1-dimensional model of negative ion photodetachment. Let m be the electron mass, and assume the electron-atom potential energy is an attractive delta function, V(x)= - V. S(x) with coefficient -V.. (b) Now suppose a weak time-dependent perturbing electric field is applied along the x-axis, equal to E(t)= E, exp(-i w t) +c.c.; Find the energy-normalized final state eigenfunctions for the unperturbed Hamiltonian, having odd parity. (c) Using the Golden Rule, calculate the photodetachment rate as a function of (hbar w) in these units, i.e. calculate the probability per unit time in these units for the electron to escape to infinity. Glve an analytic expression and plot it from 0 final state energy up to an energy | 10 E(ground)], i.e. for frequencies that reach up to a final state energy that is 10 times the absolute value of the ground state energy. For making a plot of these numerical values, use Vo =0.03 and a field strength amplitude Eo=0.0002.

Problem 1. Consider the following 1-dimensional model of negative ion photodetachment. Let m be the electron mass, and assume the electron-atom potential energy is an attractive delta function, V(x)= - V. S(x) with coefficient -V.. (b) Now suppose a weak time-dependent perturbing electric field is applied along the x-axis, equal to E(t)= E, exp(-i w t) +c.c.; Find the energy-normalized final state eigenfunctions for the unperturbed Hamiltonian, having odd parity. (c) Using the Golden Rule, calculate the photodetachment rate as a function of (hbar w) in these units, i.e. calculate the probability per unit time in these units for the electron to escape to infinity. Glve an analytic expression and plot it from 0 final state energy up to an energy | 10 E(ground)], i.e. for frequencies that reach up to a final state energy that is 10 times the absolute value of the ground state energy. For making a plot of these numerical values, use Vo =0.03 and a field strength amplitude Eo=0.0002.