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[Hell-Rell]

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[*RiC3xBoy*]

Quantum mechanics is a more fundamental theory than Newtonian mechanics and classical electromagnetism, in the sense that it provides accurate and precise descriptions for many phenomena that these "classical" theories simply cannot explain on the atomic and subatomic level. It is necessary to use quantum mechanics to understand the behavior of systems at atomic length scales and smaller. For example, if Newtonian mechanics governed the workings of an atom, electrons would rapidly travel towards and collide with the nucleus. However, in the natural world the electron normally remains in a stable orbit around a nucleus -- seemingly defying classical electromagnetism.

Quantum mechanics was initially developed to explain the atom, especially the spectra of light emitted by different atomic species. The quantum theory of the atom developed as an explanation for the electron's staying in its orbital, which could not be explained by Newton's laws of motion and by classical electromagnetism.

Quantum mechanics uses complex number wave functions (sometimes referred to as orbitals in the case of atomic electrons), and more generally, elements of a complex vector space to explain such effects. These are related to classical physics largely through probability. Probability in the context of quantum mechanics has to do with the likelihood of finding a system in a particular state at a certain time, for example, finding an electron, in a particular region around the nucleus at a particular time. Therefore, electrons cannot be pictured as localized particles in space but rather should be thought of as "clouds" of negative charge spread out over the entire orbit. These clouds represent the regions around the nucleus where the probability of "finding" an electron is the largest. This probability cloud obeys a quantum mechanical principle called Heisenberg's Uncertainty Principle, which states that there is an uncertainty in the classical position of any subatomic particle, including the electron; so instead of describing where an electron or other particle is, the entire range of possible values is used, describing a probability distribution. So in normal atoms with electrons in stationary states, the probability of the electron being within the nucleus (or somewhere else in atom within similarly small volume) is nearly zero according to the Uncertainty Principle (it is nearly zero as the nucleus has a volume and is not a point). Therefore, quantum mechanics, translated to Newton's equally deterministic description, leads to a probabilistic description of nature.

The other exemplar that led to quantum mechanics was the study of electromagnetic waves such as light. When it was found in 1900 by Max Planck that the energy of waves could be described as consisting of small packets or quanta, Albert Einstein exploited this idea to show that an electromagnetic wave such as light could be described by a particle called the photon with a discrete energy dependent on its frequency. This led to a theory of unity between subatomic particles and electromagnetic waves called wave-particle duality in which particles and waves were neither one nor the other, but had certain properties of both. While quantum mechanics describes the world of the very small, it also is needed to explain certain "macroscopic quantum systems" such as superconductors and superfluids.

Broadly speaking, quantum mechanics incorporates four classes of phenomena that classical physics cannot account for: (i) the quantization (discretization) of certain physical quantities, (ii) wave-particle duality, (iii) the uncertainty principle, and (iv) quantum entanglement. Each of these phenomena will be described in greater detail in subsequent sections.

Most physicists believe that quantum mechanics provides a correct description for the physical world under almost all circumstances. However, the effects of quantum mechanics are generally not significant when considering the observable Universe as a whole. This is because although atoms and subatomic particles are the building blocks of matter, when analyzing the universe on large scales one finds that the dominant force becomes gravity -- which is described using Einstein's general theory of relativity. In some cases, both general relativity and quantum mechanics converge. As an example, general relativity is unable to explain what will happen if a subatomic particle hits the singularity of a black hole which is a phenomenon predicted by general relativity and involves gravity in the macro world. Only quantum mechanics can provide the answer: the particle's position will have an uncertainty that follows the Heisenberg Uncertainty Principle, such that it might not really reach the singularity and thus escape the possible collapse to infinite density.

It is believed that the theories of general relativity and quantum mechanics, the two great achievements of physics in the 20th century, contradict one another for two main reasons. One is that the former is an essentially deterministic theory and the latter is essentially indeterministic. Secondly, general relativity relies mainly on the force of gravity while quantum mechanics relies mainly on the other three fundamental forces, those being the strong, the weak, and the electromagnetic. The question of how to resolve this contradiction remains an area of active research (see, for example, quantum gravity).

In certain situations, the laws of classical physics approximate the laws of quantum mechanics to a high degree of precision. This is often expressed by saying that in case of large quantum numbers quantum mechanics "reduces" to classical mechanics and classical electromagnetism . This situation is called the correspondence, or classical limit.

Quantum mechanics can be formulated in either a relativistic or non-relativistic manner. Relativistic quantum mechanics (quantum field theory) provides the framework for some of the most accurate physical theories known. Still, non-relativistic quantum mechanics is also used due to its simplicity and when relativistic effects are relatively small. We will use the terms quantum mechanics, quantum physics, and quantum theory synonymously, to refer to both relativistic and non-relativistic quantum mechanics. It should be noted, however, that certain authors refer to "quantum mechanics" in the more restricted sense of non-relativistic quantum mechanics. Also, in quantum mechanics, the use of the term particle refers to an elementary or subatomic particle.