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​A perturbation​is applied to a rigid rotator undergoing a rotational motion in a plane. The first order energy correction to the ground state is
Question

​A perturbation

​is applied to a rigid rotator undergoing a rotational motion in a plane. The first order energy correction to the ground state is

A.

B.

C.

D.

Correct option is C

Time-independent perturbation theory

In perturbation theory, we suppose that the Hamiltonian for the problem we are trying to solve,

can be expressed as the sum of a simple Hamiltonian,

which has known eigenvalues and eigenfunctions, and a contribution,

which represents the extent to which the true Hamiltonian differs from the ‘model’ Hamiltonian:

​In time-independent perturbation theory, the perturbation is always present and unvarying. For example, it might represent a dip in the potential energy of a particle in a box in some region along the length of the box. In time-independent perturbation theory, we suppose that the true energy of the system differs from the energy of the simple system, and that we can write

The first-order corrections to the energy of the ground state 

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