# Polarizability of a single hydrogen atom

• Cranky
In summary, polarizability is a measure of an atom or molecule's ability to form induced dipoles in response to an external electric field. It is calculated by dividing the induced dipole moment by the applied electric field strength and is affected by factors such as atom size, number of electrons, and external field strength. The polarizability of a single hydrogen atom is important for understanding the behavior of atoms and molecules in electric fields and is relatively small compared to other elements.
Cranky

## Homework Statement

the problem text is attached

## The Attempt at a Solution

I have solved Schrödingen equation, while getting
psi(x)=c1*cos(kx)+c2*sin(kx), where k=sqrt(2Em)/hbar
I cannot understand which boundary conditions I schould use.

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Bump; is the approach to use perturbation theory with the Stark effect?

## 1. What is polarizability?

Polarizability is a measure of the ability of an atom or molecule to form instantaneous dipoles in response to an external electric field.

## 2. How is polarizability calculated?

Polarizability is calculated as the ratio of the induced dipole moment to the applied electric field strength. For a single hydrogen atom, it is calculated using quantum mechanical equations that take into account the electron density distribution and the distance between the nucleus and the electron.

## 3. What factors affect the polarizability of a single hydrogen atom?

The polarizability of a single hydrogen atom is affected by the size of the atom, the number of electrons, and the distance between the nucleus and the electron. It also depends on the external electric field strength and the orientation of the atom in the field.

## 4. Why is the polarizability of a single hydrogen atom important?

The polarizability of a single hydrogen atom is important because it is a fundamental property that affects the behavior of atoms and molecules in electric fields. It is also used in calculations to understand and predict the properties of materials and chemical reactions.

## 5. How does the polarizability of a single hydrogen atom compare to other elements?

The polarizability of a single hydrogen atom is relatively small compared to other elements, such as noble gases and heavier atoms. This is because hydrogen has only one electron and a small atomic size, making it less likely to form induced dipoles in response to an external electric field.

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