Table of Contents

## What is the principle of perturbation theory?

The principle of perturbation theory is to study dynamical systems that are small perturbations of `simple’ systems. Here simple may refer to `linear’ or `integrable’ or `normal form truncation’, etc. In many cases general `dissipative’ systems can be viewed as small perturbations of Hamiltonian systems.

## Why there is no first order Stark effect for hydrogen?

First order Atoms and molecules possessing inversion symmetry do not have a (permanent) dipole moment and hence do not show a linear Stark effect. states, are odd under parity. Hence hydrogen-like atoms with n>1 show first-order Stark effect.

## What is the application of perturbation theory?

One of the most important applications of perturbation theory is to calculate the probability of a transition between states of a continuous spectrum under the action of a constant (time-independent) perturbation.

## What is the value of J in the perturbation theory for he atom?

Eh=4.359×10−18J=27.21eV.

## What are the first order energy shifts due to this perturbation?

The shift in energy induced by a perturbation is given to first order by the expectation value of the perturbation with respect to the unperturbed state. Thus first order time independent perturbation is equivalent to making the approximation that the wavefunction does not change.

## What is first order correction in perturbation theory?

For the first-order perturbation, we need solve the perturbed Hamiltonian restricted to the degenerate subspace D, simultaneously for all the degenerate eigenstates, where are first-order corrections to the degenerate energy levels, and “small” is a vector of orthogonal to D. This amounts to diagonalizing the matrix.

## What is second order Stark effect?

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. The Stark effect is responsible for the pressure broadening (Stark broadening) of spectral lines by charged particles.