Suchergebnisse
Suchergebnisse:
Learn how an external electric field shifts the energy levels of hydrogen atoms in the strong field limit. See the selection rules, degenerate perturbation theory, and the wave functions of the perturbed states.
- 30KB
- 3
The Stark e ect is the electric analogue to the Zeeman e ect, i.e., a particle carrying an electric dipole moment, like the H-atom, will get a splitting of its energy levels when subjected to an exterior electric eld.
- 444KB
- 8
As a more involved example of the level degeneracy lifting by a perturbation, let us discuss the Stark effect \(^{6}\) - the atomic level splitting by an external electric field. Let us study this effect, in the linear approximation, for a hydrogen-like atom/ion. Taking the direction of the external electric field
This PDF file is a chapter from a book on atomic physics, covering the interaction of atoms with static electric fields. It explains the linear and quadratic Stark effects, their quantum and classical descriptions, and their differences for hydrogen and other atoms.
- 1 The Stark Effect Hamiltonian
- 2 Perturbative Treatment of The Linear Stark Effect For A One-Electron Atom
- 3 The Linear Stark Effect, For A One-Electron Atom, with Parabolic Coordinates
If we take the non-relativistic Hamiltonian for a one-electron atom, and add the Stark effect potential energy from (12.2), we get the following Schrödinger equation: An effect of the last term in the Hamiltonian is that the potential energy will go to minus infinity for large negative values of z. This has a couple of consequences. One is that the...
To exemplify a perturbation calculation of the linear Stark effect for a hydrogenic atom, we take the simplest example possible, that is, the excited states for which n = 2. What we have to do is to apply the perturbation \(H_{\mathrm {St}}=\mathcal {E}z\) to the hydrogenic wave functions ψ200, ψ21−1, ψ210 and ψ211, using degenerate perturbation th...
The perturbation calculations emanating from the standard zero-order solutions to the one-electron Schrödinger equation (in spherical coordinates), works fine for relatively low principal quantum numbers. For larger n, another approach is more suitable. This is one in which coordinates and the corresponding quantisations are chosen such that the St...
- Anders Kastberg
- 2020
5. PERTURBATION THEORY AND STARK EFFECT 387 Before discussing the wave function in arbitrary representation, we shall say a few words about the eigenfunctions of a continuous quantity A in A-representation, i.e. in eigenrepresentation. Above we have written the wave functions in co-ordinate representation. In eigenrepresentation they are
Learn how external electric fields affect the energy levels and eigenstates of hydrogen and alkali atoms, using perturbation theory and symmetry principles. See plots, formulas and examples of the Stark effect in this PDF document.
