The Stark effect refers to the shifting and splitting of spectral lines in the presence of an external electric field. This phenomenon was discovered by the German physicist Johannes Stark in 1913. The Stark effect is an important aspect of atomic and molecular physics, and it provides insights into the interaction between charged particles and electric fields. We consider hydrogen atom . Hamiltonian operator of electron

The electron and nucleus forms a dipole having dipole moment

Here r is directed away from the nucleus but vector p is directed from negative to positive charge. When electric field is applied to the atom, the dipole gains energy.

If E is in z direction corresponding Hamiltonian operator.

The eigen kets of Ho are l nlm>. if the atom is in ground state, n =1 , l=1, m= 0. So the eigen ket of Ho for the atom in ground state is l 1 0 0>

So to find the first order correction to energy, we use non degenerate perturbation theory.

Since the integrand is odd function and the limit with z are symmetric with reference to origin.

The first order correction to energy is zero is due to the fact that there is no permanent electric dipole of the atom when it is in ground state. The direction of the dipole moment is continuously changing. Now we consider second order correction to energy.

n = 1

So second order correction to energy is proportional to square of electric field when the atom is in ground state.

Now, we consider the correction to energy when the atom is in first higher state (n=2)

The possible eigen state of Ho are n=2, l = 1

So we have to use degenerate perturbation theory. The basis kets are

l 2 0 0> l 2 1 1> l 2 1 0> l 2 1 -1 >

Now,

Here are the key features of the Stark effect:

Energy Shift: When an atom or molecule is subjected to an external electric field, the energy levels of its electrons are shifted. The energy shift is proportional to the strength of the electric field.

Line Splitting: In addition to the energy shift, spectral lines can split into multiple components. The degree of splitting depends on the quantum numbers associated with the atomic or molecular energy levels and the characteristics of the external electric field.

Polarization of Lines: The Stark effect can also induce polarization in spectral lines. The orientation of the polarization depends on the direction of the electric field with respect to the direction of observation.

Stark Hamiltonian: The Stark effect is often described using the Stark Hamiltonian, a perturbation term added to the Hamiltonian of the system to account for the interaction with the external electric field. The Stark Hamiltonian includes terms related to the electric dipole moment of the system.

Applications

The Stark effect has applications in various areas of physics, including atomic and molecular spectroscopy. It is used to study the electric properties of atoms and molecules, and it has practical applications in devices such as lasers and frequency standards.

The Stark effect is complementary to the Zeeman effect, which describes the splitting of spectral lines in the presence of an external magnetic field. Both effects are important in understanding the behaviour of atoms and molecules in the presence of external fields, providing valuable information about their electronic structure and properties.

This note is a part of the Physics Repository.

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