Blochsfääri

Blochsfääri is a theoretical concept used in quantum mechanics, specifically in the description of electrons in periodic potentials, such as those found in crystals. It represents the state of an electron in a crystal lattice. Mathematically, a Bloch wave is characterized by a wave vector k and a crystal momentum. The Bloch sphere is a generalization of the Bloch sphere used for spin-1/2 particles, which is a simple sphere. For systems with more complex internal degrees of freedom, the Bloch sphere can become a more complex manifold.

The Bloch sphere is a geometrical representation of the possible quantum states of a two-level system, also known as a qubit. For a spin-1/2 particle, any state can be represented as a point on the surface of a sphere. The North Pole typically represents the spin-up state, and the South Pole represents the spin-down state. Other points on the sphere represent superpositions of these two states.

In the context of solids, Bloch's theorem states that the wave function of an electron in a periodic potential can be written as a product of a plane wave and a periodic function with the same periodicity as the lattice. These wave functions are called Bloch waves. The wave vector k in a Bloch wave is related to the electron's momentum but is defined within the first Brillouin zone. The Bloch sphere provides a geometrical way to visualize and understand the evolution of these quantum states, particularly under the influence of external fields or perturbations. It's a fundamental tool for comprehending electron behavior in crystalline materials and forms the basis for understanding phenomena like band structures and quantum transport.