# Unraveling Weak Field Stark Effect in Hydrogen

• PHamnett
In summary, the conversation discusses the use of degenerate perturbation theory to show that a weak external field causes a shift in the energy levels of the four j = 1/2 states of hydrogen. The equations <1 1/2 1/2 | z | 0 1/2 1/2> = -\sqrt{1/3}<1 0 | z | 0 0> and <1 1/2 -1/2 | z | 0 1/2 -1/2> = \sqrt{1/3}<1 0 | z | 0 0> are used to construct a perturbed Hamiltonian, but the reasoning behind these equations is unclear
PHamnett

## Homework Statement

Considering the n = 2 states of hydrogen: In the absense of an external field, the four j = 1/2 states are degenerate. Using degenerate pertubation theory, I am supposed to show that for a very weak field the Stark effect shifts the energy levels by

$$\mp \sqrt{3}a_0 e \epsilon$$

where $$a_0$$ is the bohr radius, e is the electric charge and $$\epsilon$$ is the electric field

The solutions state that we should get the following equations:
<1 1/2 1/2 | z | 0 1/2 1/2> = $$-\sqrt{1/3}$$<1 0 | z | 0 0>

and

<1 1/2 -1/2 | z | 0 1/2 -1/2> = $$\sqrt{1/3}$$<1 0 | z | 0 0>

and then from there a pertubed hamiltonian is constructed.

But to be honest, none of it seems to make sense and me and my friend do not know where even the first line of the solutions comes from. Yet alone the rest.
Any light that could be shed on the situation would be most appreciated.
Thanks.

What term is being added to the unperturbed Hamiltonian? Start by figuring that out. Then it should be clear why you need to find the matrix elements of z.

## 1. What is the Weak Field Stark Effect in Hydrogen?

The Weak Field Stark Effect in Hydrogen is the phenomenon where the energy levels of a hydrogen atom are shifted in the presence of an electric field. This effect occurs due to the interaction between the electric field and the electric dipole moment of the atom.

## 2. Why is it important to study the Weak Field Stark Effect in Hydrogen?

Studying the Weak Field Stark Effect in Hydrogen allows scientists to better understand the fundamental principles of quantum mechanics and the behavior of atoms in the presence of external fields. It also has practical applications in areas such as spectroscopy and atomic clocks.

## 3. How is the Weak Field Stark Effect in Hydrogen experimentally observed?

The Weak Field Stark Effect in Hydrogen is observed by measuring the energy levels of the hydrogen atom in the presence of an electric field. This can be done using techniques such as spectroscopy or by measuring the deflection of a beam of hydrogen atoms in an electric field.

## 4. What factors affect the strength of the Weak Field Stark Effect in Hydrogen?

The strength of the Weak Field Stark Effect in Hydrogen is affected by the magnitude and direction of the electric field, as well as the energy levels of the atom. The effect is stronger for higher energy levels and for stronger electric fields.

## 5. How does the Weak Field Stark Effect in Hydrogen differ from the Strong Field Stark Effect?

The Weak Field Stark Effect in Hydrogen occurs in the presence of a weak electric field, where the energy levels of the atom are only slightly shifted. In contrast, the Strong Field Stark Effect occurs in the presence of a strong electric field, causing large shifts in the energy levels and even ionization of the atom.

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