i hope this slide will help you

1.  @Asan Fizika
 @fizika_physics

2. What do we mean by stark effect ?
The Stark effect is the shifting and splitting of
spectral lines of atoms and molecules due to the
presence of an external electric field. The amount
of splitting or shifting is called the Stark splitting
or Stark shift.
In general, one distinguishes first- and second-
order Stark effects.
The first-order effect is linear in the applied
electric field, while the second-order effect is
quadratic in the field.

4. The Stark Effect is shown here in the splitting and shifting
of spectral lines in hydrogen under the influence of an
external electric field.

5. History of the Stark Effect
When Zeeman discovered the effect of
magnetic fields on the wavelengths of
emitted spectra from an excited gas, the
Zeeman effect, it sparked a search for a
similar effect due to electric fields.
For 15 years the search failed to show such
an effect and as a matter of fact.

6. Experimental failure to find the effect of electric
fields on emitted spectra was actually due to a very
simple phenomenon. Excitation of atoms to show
spectra was usually performed by passing an electric
arc through a gas.
The gas would be ionized allowing current to flow
via motion of the freed electrons and collisions
between electrons and ions or electrons and neutral
atoms would excite the ions or atoms and then
spectra would be visible as the ions or atoms
decayed back down from their excited states.
The problem is that applying an external electric
field to this highly conductive gas

7. Johannes Stark, in 1913, recognized
the importance of lowering the
conductivity of the luminous gas in
order to maintain a strong electric
field within the gas.
Stark observed with a spectroscope
that the characteristic spectral lines,
called Balmer lines, of hydrogen were
split into a number of symmetrically
spaced components.

8. Balmer series
The Balmer series or Balmer lines in atomic
physics, is the designation of one of a set of 6
different named series describing the spectral
line emissions of the hydrogen atom.
The Balmer series is calculated using the
Balmer formula, an empirical equation
discovered by Johann Balmer in 1885.

9. The Balmer series is characterized by the electron
transitioning from n ≥ 3 to n = 2, where n refers to
the radial quantum number or principal quantum
number of the electron.
The transitions are named sequentially by Greek
letter:
n=3 to n=2 is called H-α(656 nm),
from n=4 to n= 2 is H-β(486 nm),
from n=5 to n=2 is H-γ(434 nm),
and from n=6 to n=2 is H-δ(410 nm).
There are also multiple ultraviolet Balmer lines
that have wavelengths shorter than
400 nm.

11. Figure in the previous slide shows the
quantized orbits of the hydrogen atom for
n= 1 through 5.
Each orbit corresponds to a definite energy
state of the atom.
The straight lines originating on the n=
3, 4, and 5 orbits and terminating on the
n= 2 orbit represent transitions in the
Balmer series.

12. Later, it was discovered that when the
Balmer series lines of the hydrogen
spectrum were examined at very high
resolution, they were closely spaced
doublets.
This splitting is called fine structure. It was
also found that excited electrons from
shells with n greater than 6 could jump to
the n = 2 shell, emitting shades of
ultraviolet when doing so.

13. Hydrogen Atom Ground State in
an E-field, the Stark Effect.
We have solved the Hydrogen problem with
the following Hamiltonian
Now we want to find the correction to that solution
if an Electric field is applied to the atom. We
choose the axes so that the Electric field is in the z-
direction. The perturbation is then:

14. It is typically a small perturbation. For non-degenerate
states, the first order correction to the energy is zero
because the expectation value of z is an odd function.
 First order correction (n=1) : Since,
To use perturbation theory, we’ll need the wave
functions for unperturbed hydrogen, which are given
in Griffiths as equation 4.89. For the ground state
n = 1, we have

16.  We therefore need to calculate the second order
correction. This involves a sum over all the other
states.
We need to compute all the matrix elements of z
between the ground state and the other Hydrogen
states.

17. References:
• H. Friedrich, Theoretical Atomic Physics, (1990).
• E. U. Condon and G. H. Shortley, The Theory of
Atomic Spectra, (1935).
• A. Sommerfeld , Atomic Structure and Spectral
Lines, London: Methuen (1923).
• H. E. White, Introduction to atomic spectra,
(1934).
• C. R. Nave, Hydrogen Spectrum, (2006).
• J. Griffiths, David Introduction to Quantum
Mechanics, 2nd Ed (2005).
• A. McGraw-Hill, Perspectives of Modern Physics,
(1969).

18. THANK YOU
FOR YOUR
ATTENTION.