Discussions on Quantum Mechanics

 Discussions on Quantum Mechanics

Any discussion on Quantum Mechanics requires a working knowledge of the following terms. The terms and their definitions are provided in this post for assistance in future discussions on Quantum Mechanics.

Quantum Object

A quantum object is a fundamental unit of matter or energy, such as, atoms, ions, electrons, and photons that is treated as being part of a quantum system.

Quantum System

A quantum system is a system that obeys the laws of quantum mechanics, or the quantum principles.

Quantum Principles

The quantum principles are: (a) Wave-Particle Duality, (b) Quantization, (c) Uncertainty Principle, (d) Superposition, and (e) Quantum Entanglement.

Wave-Particle Duality

Wave-particle duality is a fundamental concept in quantum mechanics that describes the dual nature of quantum objects exhibiting both wave-like and particle-like properties depending on the experimental circumstances.

Quantization

Quantization is a fundamental principle in quantum mechanics that describes how certain physical properties are restricted to discrete values rather than continuous ranges.

Uncertainty Principle

The Uncertainty Principle is a fundamental concept in quantum mechanics that states there is a limit to the precision with which certain pairs of physical properties of a particle can be simultaneously known. This principle applies to complementary variables such as position and momentum, or energy and time.

Superposition

Superposition is a fundamental concept in quantum mechanics that describes the ability of quantum systems to exist in multiple states simultaneously until it is measured. It is mathematically represented as a linear combination of all possible states of a system. This principle is a direct consequence of the linear nature of the Schrödinger equation, which allows for linear combinations of solutions to represent valid quantum states.

Quantum Entanglement

Quantum entanglement is a fundamental principle in quantum mechanics where two or more particles become inextricably linked, sharing a collective quantum state even when separated by vast distances.

Quantum State

A quantum state is a mathematical representation that embodies the complete knowledge of a quantum system. It describes the physical properties and behavior of quantum objects. It is inherently probabilistic in nature.

Quantum Numbers

Quantum numbers are used to describe a quantum state. These are discrete values that describe specific properties of the system. For electrons in atoms, these typically include: (a) Principal quantum number, (b) Angular momentum quantum number, (c) Magnetic quantum number, and (d) Spin quantum number.

Schrödinger Equation

The Schrödinger equation is the fundamental equation that describes the behavior of quantum systems. Just as Newton's second law governs classical mechanics, the Schrödinger equation governs quantum mechanics. It provides a mathematical framework to determine the wave function of a quantum system.

Wave Function

A wave function is a fundamental concept in quantum mechanics that describes the quantum state of a particle or system. It is a mathematical function that encapsulates all the measurable information about a quantum object. The square of the wave function's magnitude represents the probability density of finding the particle at a specific position and time.

Wave Function Collapse

Wave function collapse describes the transition of a quantum system from a superposition of multiple states to a single definite state upon measurement or observation. This phenomenon occurs when a wave function, initially representing various possible states of a quantum system, abruptly reduces to one specific eigenstate. The probability of collapsing to a particular state is determined by the wave function before the collapse.

Observable

An observable is a physical property or quantity, such as, position, momentum, angular momentum, spin, etc., that can be measured. Observables play a crucial role in describing and understanding quantum systems.

Eigenstate

An eigenstate is a specific quantum state of a system for which a particular observable has a definite, predictable value. When a quantum system is in an eigenstate of an observable, any measurement of that observable will always yield the same result, known as the eigenvalue. Eigenstates are solutions to the time-independent Schrödinger equation.

Eigenvalue

The eigenvalues of an observable operator correspond to the possible outcomes of a measurement of that observable. When a measurement is performed, the quantum state "collapses" into one of the eigenstates of the observable being measured.