(a) Derive the following general relation for the first order correction to the energy, E, in time-independent perturbation theory %3D where the y are the eigen-functions of the unperturbed Hamiltonian Ho and H' is the time independent perturbation. (b) A particle moves in a potential given by Vo sin(ax/a) for 0 < x < a V = otherwise where Vo is a small constant. Treat this as a perturbation for the case of a particle in an infinitely deep square well of width a and calculate the change in energy of the lowest energy state to first order in Vo.
(a) Derive the following general relation for the first order correction to the energy, E, in time-independent perturbation theory %3D where the y are the eigen-functions of the unperturbed Hamiltonian Ho and H' is the time independent perturbation. (b) A particle moves in a potential given by Vo sin(ax/a) for 0 < x < a V = otherwise where Vo is a small constant. Treat this as a perturbation for the case of a particle in an infinitely deep square well of width a and calculate the change in energy of the lowest energy state to first order in Vo.
Related questions
Question
Transcribed Image Text:(a) Derive the following general relation for the first order correction to the energy,
E, in time-independent perturbation theory
where the 0 are the eigen-functions of the unperturbed Hamiltonian Ho and H'
is the time independent perturbation.
(b) A particle moves in a potential given by
Vo sin(ax/a) for 0 < x < a
V :
%D
otherwise
where Vo is a small constant. Treat this as a perturbation for the case of a particle
in an infinitely deep square well of width a and calculate the change in energy of
the lowest energy state to first order in Vo.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
