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The unperturbed energies (in eV) of a three-level system are . The matrix elements of a perturbation V (in eV) between the levels (in subscript) are .
Question



The unperturbed energies (in eV) of a three-level system are

. The matrix elements of a perturbation V (in eV) between the levels (in subscript) are

. The second-order correction to the ground state energy (in eV) in the presence of perturbation V is

A.

– 25/4

B.

−67

C.

−17

D.

−16

Correct option is C


Perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy levels and eigenstates) can be expressed as "corrections" to those of the simple system. These corrections, being small compared to the size of the quantities themselves, can be calculated using approximate methods. The complicated system can therefore be studied based on knowledge of the simpler one. In effect, it is describing a complicated unsolved system using a simple, solvable system.
In quantum mechanics, the second-order perturbation correction to the ground state energy of a system is given by:

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