Time-independent perturbation theory. (a) explain the need and the scope of application (b) if a perturbation is introduced a a,+with a«1 expand eigenvalue of energy and cigenfunction to produce three schrödinger equations (se) for the 0-th, 1-st, and 2-nd order in (c) expressing eigenfunction as a liner combination of the eigenfunctions of the unpertubed se derive the first order correction to the eigenenergy (d) using similar approach, derive the second order correction to the eigenenergy (e) derive the new perturbed eignefunction corrected to the first order

1. what is the relationship between wavelength and the penetrating power of an electromagnetic wave? a) the penetrating power has no relationship to the wavelength. b) the penetrating power increases as the wavelength increases. c) the penetrating power decreases as the wavelength increases. d) the penetrating power decreases as the wavelength decreases. 2. as ice melts and turns into water, the speed of sound through the material would most likely do what? justify your answer. a) the speed would not change because the material is always water. b) the speed of sound would increase because the density of water is less than that of ice. c) the speed of sound would increase because energy is added to ice in order to make it melt. d) the speed of sound would decrease because sound travels faster through solids than liquids. 3.which of these waves need a medium to travel through? a) sound b) x-rays c) infrared rays d) visible light