Quantum Physics Key Principles

Wave-Particle Duality: Quantum objects (e.g., electrons, photons) can exhibit both wave-like and particle-like behavior.
Uncertainty Principle: It is impossible to know certain properties (e.g., position, momentum) simultaneously with infinite precision.
Superposition: Quantum objects can exist in multiple states simultaneously.
Entanglement: Quantum objects can be connected in such a way that the state of one object affects the state of the other, even when separated by large distances.

Schrödinger Equation: A mathematical equation that describes the time-evolution of a quantum system.
Wave Function: A mathematical function that describes the quantum state of a system.
Hamiltonian: A mathematical operator that represents the total energy of a quantum system.

Atomic Physics: The study of the behavior of electrons in atoms.
Molecular Physics: The study of the behavior of electrons in molecules.
Condensed Matter Physics: The study of the behavior of electrons in solids and liquids.

Quantum Tunneling: The ability of a quantum object to pass through a potential energy barrier.
Quantum Fluctuations: Temporary and random changes in energy that occur at the quantum level.
Quantum Decoherence: The loss of quantum coherence due to interactions with the environment.

Quantum Computing: The use of quantum mechanics to perform calculations beyond the capabilities of classical computers.
Quantum Cryptography: The use of quantum mechanics to create secure encryption methods.
Quantum Teleportation: The transfer of quantum information from one location to another without physical transport of the information.

Wave-Particle Duality: Exhibits both wave-like and particle-like behavior, depending on observation, e.g., electrons and photons.
Uncertainty Principle: Impossible to know certain properties, such as position and momentum, simultaneously with infinite precision.
Superposition: Can exist in multiple states simultaneously, e.g., spin up and spin down.
Entanglement: Connected in such a way that the state of one object affects the state of the other, even when separated by large distances.

Schrödinger Equation: Mathematical equation that describes the time-evolution of a quantum system, providing the probability of finding a system in a particular state.
Wave Function: Mathematical function that describes the quantum state of a system, encoding all the information about the system.
Hamiltonian: Mathematical operator that represents the total energy of a quantum system, including kinetic and potential energy.

Atomic Physics: Study of electron behavior in atoms, including energy levels and electron spin.
Molecular Physics: Study of electron behavior in molecules, including bonding and molecular orbitals.
Condensed Matter Physics: Study of electron behavior in solids and liquids, including crystal structures and phase transitions.

Quantum Tunneling: Ability of a quantum object to pass through a potential energy barrier, e.g., in scanning tunneling microscopy.
Quantum Fluctuations: Temporary and random changes in energy that occur at the quantum level, affecting the behavior of particles.
Quantum Decoherence: Loss of quantum coherence due to interactions with the environment, causing the loss of quantum behavior.

Quantum Computing: Use of quantum mechanics to perform calculations beyond the capabilities of classical computers, e.g., simulating complex systems.
Quantum Cryptography: Use of quantum mechanics to create secure encryption methods, e.g., quantum key distribution.
Quantum Teleportation: Transfer of quantum information from one location to another without physical transport of the information, e.g., in quantum communication.

Wave-particle duality suggests that particles can exhibit both wave-like and particle-like behavior, depending on how they are observed.
Wave-like behavior is demonstrated through:
- Diffraction, where particles bend around obstacles
- Interference, where particles exhibit interference patterns
Particle-like behavior is demonstrated through:
- The photoelectric effect, where particles behave as particles when interacting with light
- Electron diffraction, where particles behave as particles when passing through a crystal lattice

Energy is quantized, meaning it comes in discrete packets (quanta) rather than being continuous.
Quantization is observed in:
- Photon energy, which is quantized according to the formula E=hf, where E is energy, h is Planck's constant, and f is frequency
- Electron energy levels, which are quantized with specific energy values for each level in an atom

A wave function (ψ) is a mathematical description of a quantum system, describing the probability of finding a particle in a given state.
Probability density (|ψ(x)|²) is the probability of finding a particle at a given point (x).
Wave functions are normalized to ensure the total probability of finding the particle is 1.

The Schrödinger equation is a mathematical equation that describes the time-evolution of a quantum system.
The equation is written as: iℏ(∂ψ/∂t) = Hψ, where H is the Hamiltonian operator.
The Schrödinger equation is used to determine the wave function and probability density of a quantum system.

Superposition is the ability of a quantum system to exist in multiple states simultaneously.
Entanglement occurs when two or more quantum systems become correlated, with the state of one system dependent on the state of the other.
Measuring the state of one system instantly affects the state of the other, regardless of distance.

Pauli's Exclusion Principle states that no two electrons in an atom can have the same set of quantum numbers (n, l, m, s).
This principle explains the periodic table and the structure of atoms.

Angular momentum (L) is a measure of the tendency of an object to continue rotating.
In quantum mechanics, angular momentum is quantized, with specific values for each energy level.
The spin of an electron is a fundamental property, with a spin of ½ ħ.