Quantum Mechanics in Solids: Bloch's Theorem

This set of flashcards covers key concepts related to quantum mechanics in solids, focusing on Bloch's theorem, the Kronig-Penney model, and related physical properties.

Kronig-Penney Model

A model that describes particles in a periodic potential using a simplified one-dimensional approximation.

Bloch's Theorem

States that the wave functions of electrons in a periodic potential can be expressed as a plane wave modulated by a periodic function.

Periodic Potential

A potential that repeats itself at regular intervals, affecting how particles, like electrons, behave within a solid.

Effective Mass

A quantity that characterizes the response of a particle in a periodic potential, reflecting how inert the particle behaves under an external force.

Brillouin Zone

A defined volume in reciprocal space that contains all the unique wave vectors for a crystallographic lattice.

Fermi Energy

The energy of the highest occupied molecular orbital at absolute zero temperature, representing the energy level of electrons in a solid.

Energy Band

The range of energy levels that electrons can occupy in a solid, separated by forbidden energy gaps.

Forbidden Gap

An energy range where no electron states can exist, separating the allowed energy bands.

Wave Function

A mathematical function that describes the quantum state of a particle and contains all the information about the system.

Schrödinger Equation

Fundamental equation of quantum mechanics that describes how the quantum state of a physical system changes over time.

Electron Density

The probability of finding an electron in a given volume of space and is related to the number of electrons in the system.

Quantum Well

A potential well that confines particles, such as electrons, in a small space, leading to quantized energy levels.

Density of States

The number of states per interval of energy at each energy level that are available to be occupied by electrons.

Mean Free Path

The average distance traveled by a particle between collisions, significant for understanding conductivity in metals.

Wiedemann-Franz Law

A law stating that the ratio of thermal conductivity to electrical conductivity is proportional to the temperature.

Thermal Conductivity

The property of a material to conduct heat, often related to the movement of electrons in metals.

Ohm's Law

Describes the relationship between voltage, current, and resistance in an electrical circuit.

Specific Resistance

A measure of how strongly a material opposes the flow of electric current, defined per unit length and area.

Mobile Charge Carrier

Electrons or holes that are free to move through a material and conduct electricity.

Conductivity

A measure of a material's ability to conduct an electric current.