Energy and Wave Function of A Free Electron
For a free particle the potential is . The Schrödinger equation for such a particle, like the free electron, is
The wave function can be split into a solution of a time dependent and a solution of a time independent equation. The solution of the time dependent equation is
with energy
The solution of the time independent equation is
with a wave vector . is the volume of space where the electron can be found. The electron has a kinetic energy
The plane wave solution of this Schrödinger equation is
For solid state and condensed matter physics the time independent solution is of major interest. It is the basis of electronic band structure models that are widely used in solid-state physics for model Hamiltonians like the nearly free electron model and the Tight binding model and different models that use a Muffin-tin approximation. The eigenfunctions of these Hamiltonians are Bloch waves which are modulated plane waves.
Read more about this topic: Free Electron Model
Famous quotes containing the words energy and, energy, wave, function and/or free:
“All my energy and attention were devoted to trying to help her solve her problems. Unfortunately I didn’t have much success.”
—Arthur Miller (b. 1915)
“Since the beginning of time, three-quarters of the mental energy and of the lies inspired by vanity have been expended for their inferiors by people who are only abased by such expenditure. And Swann, who was easygoing and unaffected with a duchess, trembled at the thought of being scorned and put on airs when he was with a housemaid.”
—Marcel Proust (1871–1922)
“And his wish is intimacy,
Intimater intimacy,
And a stricter privacy;
The impossible shall yet be done,
And, being two, shall still be one.
As the wave breaks to foam on shelves,
Then runs into a wave again,
So lovers melt their sundered selves,
Yet melted would be twain.”
—Ralph Waldo Emerson (1803–1882)
“To make us feel small in the right way is a function of art; men can only make us feel small in the wrong way.”
—E.M. (Edward Morgan)
“The real American type can never be a ballet dancer. The legs are too long, the body too supple and the spirit too free for this school of affected grace and toe walking.”
—Isadora Duncan (1878–1927)