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:
“I thought a lot about our nation and what I should do as president. And Sunday night before last, I made a speech about two problems of our country—energy and malaise.”
—Jimmy Carter (James Earl Carter, Jr.)
“In the west, Apollo and Dionysus strive for victory. Apollo makes the boundary lines that are civilization but that lead to convention, constraint, oppression. Dionysus is energy unbound, mad, callous, destructive, wasteful. Apollo is law, history, tradition, the dignity and safety of custom and form. Dionysus is the new, exhilarating but rude, sweeping all away to begin again. Apollo is a tyrant, Dionysus is a vandal.”
—Camille Paglia (b. 1947)
“Now I stand as one upon a rock,
Environed with a wilderness of sea,
Who marks the waxing tide grow wave by wave,
Expecting ever when some envious surge
Will in his brinish bowels swallow him.”
—William Shakespeare (1564–1616)
““... The state’s one function is to give.
The bud must bloom till blowsy blown
Its petals loosen and are strown;
And that’s a fate it can’t evade
Unless ‘twould rather wilt than fade.””
—Robert Frost (1874–1963)
“Miracles are like jokes. They relieve our tension suddenly by setting us free from the chain of cause and effect.”
—Gerald Branan (1894–1987)