A small Consider a 2-level quantum system. Hamiltonian that describes it is given by perturbation is added in the form of H', a C b) (a) Find first-order and second-order correction to energy eigenvalues(b) Compare new energy eigenvalues with the exact eigenvalues for the perturbed system(c) Find the eigenstates of the perturbed system up to first order

(a) Find first-order and second-order correction to energy eigenvalues are solved in the attached picture below. same as (b) and (c)

(b) Compare new energy eigenvalues with the exact eigenvalues for the perturbed system

(c) Find the eigenstates of the perturbed system up to first order

The above was solved considering a 2-level quantum system.

Explanation:

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.