An Introduction to Quantum Physics
In the late nineteenth and early twentieth centuries, physicists were forced to look beyond Newtonian mechanics for a more general theory. Quantum theory arose from observations and experiments which could not be explained by an application of classical physics. Basically, quantum physics describes phenomenon that classical physics cannot: Quantization of certain physical quantities, the uncertainty principle, wave-particle duality, and quantum entanglement. These concepts, along with a few others, are defined very briefly below.
This information is not intended to be complete or comprehensive, but to provide the non-physicist with an easy-to-understand introduction to a few of the fundamental concepts of quantum theory. At the end of this post are links to websites which offer more detailed discussions and explanations of these concepts.
Basic Concepts and Definitions
- Quantum State
A quantum state is the condition in which a quantum system exists, represented by mathematical object that describes the quantum system.
An observable is a property of a system state that can be determined by some sequence of physical operations. Examples of observables include energy, position, momentum, and angular momentum.
Measurement of a quantum state is generally described by a probability distribution, determined by the quantum state and the observable describing the measurement.
Quantization is a procedure for constructing a quantum physics theory from a classical physics theory foundation by restricting a variable quantity to discrete values rather than to a continuous set of values. However, quantum physics does not assign definite values to system observables, but rather makes predictions about obtaining each of the possible outcomes from measuring those observables.
- Wave Function
A wave function is a quantum theory equation that mathematically describes the probability density of an object in space and time. It is used to describe the propagation of the wave associated with a particle or group of particles.
Superposition is the phenomenon in which a quantum system exists in all possible states simultaneously, for as long as it remains unobserved.
Entanglement describes a quantum state that is not entirely independent of other states, whether or not the individual objects are spatially separated. As a result, measurements performed on one system seem to instantaneously influence the other system(s) entangled with it, so that none of the entangled states can be considered to be isolated from one another.
Nonlocality describes the fact that objects created out of some initially mixed (or common) state will remain correlated and instantaneously “communicate” with each other even when separated by large distances. Nonlocality postulates a principle of holistic interconnectedness operating at the quantum level, contradicting the localistic assumptions of classical, Newtonian physics.
Decoherence is the mechanism by which the apparent collapse of superposition (all possible states) into a single definite state occurs, via entanglement.
An eigenstate is one of the many possible states which may exist in a quantum system prior to decoherence. When the system is observed, the quantum state appears to “jump” to a particular eigenstate, and that eigenstate is the one which is perceived.
- The Uncertainty Principle (Heisenberg)
The Uncertainty Principle states that both the position and the momentum of a particle cannot be simultaneously and precisely measured. The more precisely the position (or momentum) of a particle is measured, the less precisely one can measure what its momentum (or position) might be. This principle has profound implications for both the classical concept of cause-and-effect and the determinacy of past and future events.
- Wave-Particle Duality
A particle is an irreducible constituent of matter in space/time. It can exhibit properties including mass, electric charge, and magnetic moment which determine how it interacts in the universe. A particle travels along a linear path.
A wave is a disturbance in spacetime, which can transfer energy from one point to another. Unlike a particle, a wave can travel through a vacuum (without a medium). Instead of simply following a linear path like a particle, a wave spreads out as it travels.
In quantum physics, wave–particle duality consolidates the particle-based theories of classical physics with the observed behavior of light (apparently dualistic). It refers to the concept that all matter exhibits both wave-like and particle-like properties.
Complementarity is the concept that the underlying properties of entities may manifest themselves in contradictory forms at different times, depending on the conditions of observation. It states that a quantum object can either behave as a particle or as wave, but never simultaneously as both; that a stronger manifestation of the particle nature (wave nature) leads to a weaker manifestation of the wave nature (particle nature).
- The Schrodinger Equation
The Schrödinger equation is the fundamental equation of physics for describing quantum mechanical behavior. It is used to find the allowed energy levels of a quantum system and enables us to analytically and precisely predict the behavior of a wave function. There is a time-dependent form of this equation (used for describing progressive waves as applicable to the motion of free particles), as well as the time-independent form of this equation (used for describing standing waves).
The equation has central importance to quantum mechanics similar to that of Hamilton’s equations of motion in classical mechanics.
Getting Started with Quantum (Philip Carr)
Introduction to Quantum Theory (Quantiki)
Quantum theory: Weird and Wonderful (Physics World)
Quantum Physics Made Relatively Simple (Hans Bethe Video Lectures)
The Quantum Exchange (Tutorials and Open Source Software)