In physics, the correspondence principle is a principle, first invoked by Niels Bohr in 1923, which states that the behavior of quantum mechanical systems reduce to classical physics in the limit of large quantum numbers. Wikibooks Wikiversity has more about this subject: School of Physics sci. ... Niels Bohr Niels Henrik David Bohr (October 7, 1885 – November 18, 1962) was a Danish physicist who made essential contributions to understanding atomic structure and quantum mechanics. ... 1923 was a common year starting on Monday (link will take you to calendar). ... Fig. ... Classical mechanics is a model of the physics of forces acting upon bodies. ...

The rules of quantum mechanics are highly successful in describing microscopic objects, such as atoms and elementary particles. On the other hand, we know from experiment that a variety of macroscopic systems (springs, capacitors, llamas, and so forth) can be accurately described by classical theories such as classical mechanics and classical electrodynamics. However, it is not unreasonable to believe that the ultimate laws of physics must be independent of the size of the physical objects being described. This is the motivation for Bohr's correspondence principle, which states that classical physics must emerge as an approximation to quantum physics as systems become "larger". Properties For alternative meanings see atom (disambiguation). ... Particles explode from the collision point of two relativistic velocity (100 GeV) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... From Latin ex- + -periri (akin to periculum attempt). ... A helical or coil spring. ... Various types of capacitors A capacitor is a device that stores energy in the electric field created between a pair of conductors on which equal but opposite electric charges have been placed. ... Binomial name Lama glama (Linnaeus, 1758) The Llama (Lama glama) is a large camelid native to South America. ... Classical mechanics is a model of the physics of forces acting upon bodies. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ...

The conditions under which quantum and classical physics agree are referred to as the correspondence limit, or the classical limit. Bohr provided a rough prescription for the correspondence limit: it occurs when the quantum numbers describing the system are large, meaning either some quantum numbers of the system are excited to a very large value, or the system is described by a large set of quantum numbers, or both. The classical limit is the ability of a physical theory to approximate or recover classical mechanics when considered over special values of its parameters. ...

The correspondence principle is one of the tools available to physicists for selecting quantum theories corresponding to reality. The principles of quantum mechanics are fairly broad - for example, they state that the states of a physical system occupy a Hilbert space, but do not state what type of Hilbert space. The correspondence principle limits the choices to those that reproduce classical mechanics in the correspondence limit. For this reason, Bohm has argued that classical physics does not emerge from quantum physics in the same way that classical mechanics emerges as an approximation of special relativity at small velocities; rather, classical physics exists independently of quantum theory and cannot be derived from it. Reality in everyday usage means everything that exists. ... One of the remarkable characteristics of the mathematical formulation of quantum mechanics, which distinguishes it from mathematical formulations of theories developed prior to the early 1900s, is its use of abstract mathematical structures, such as Hilbert spaces and operators on these spaces. ... In mathematics, a Hilbert space is an inner product space that is complete with respect to the norm defined by the inner product. ... David Joseph Bohm (December 20, 1917 _ October 27, 1992) was an American quantum physicist who made significant contributions in the fields of theoretical physics, philosophy and neuropsychology, and to scientists working on the Manhattan Project. ... A simple introduction to this subject is provided in Special relativity for beginners Special relativity (SR) or the special theory of relativity is the physical theory published in 1905 by Albert Einstein. ... This article is about velocity in physics. ...

An example: the quantum harmonic oscillator

We provide a demonstration of how large quantum numbers can give rise to classical behavior. Consider the one-dimensional quantum harmonic oscillator. Quantum mechanics tells us that the (kinetic) energy of the oscillator, E, has a set of discrete values: The quantum harmonic oscillator is the quantum mechanical analogue of the classical harmonic oscillator. ...

where is the angular frequency of the oscillator. However, in a classical harmonic oscillator such as a lead ball attached to the end of a spring, we do not perceive any discreteness. Instead, the energy of such a macroscopic system appears to vary sinusoidally over a continuum of values. Angular frequency is a measure of how fast an object is rotating In physics (specifically mechanics and electrical engineering), angular frequency ω (also called angular speed) is a scalar measure of rotation rate. ... A harmonic oscillator is a mechanical system in which there exists a returning force F directly proportionate to the displacement x, i. ...

We can verify that our idea of "macroscopic" systems fall within the correspondence limit. The average kinetic energy of the classical harmonic oscillator is equal to the average potential energy, which is: Kinetic energy (also called vis viva, or living force) is energy possessed by a body by virtue of its motion. ... Potential energy (U, or Ep), a kind of scalar potential, is energy by virtue of matter being able to move to a lower-energy state, releasing energy in some form. ...

where [x²] denotes the average value of the squared displacement. Thus, the quantum number has the value

If we apply the appropriately "human-scale" values m = 1kg, = 1Hz, and [x²] = 1m, then n ≈ 4.74×10³³. This is a very large number, so the system is indeed in the correspondence limit. The international prototype, made of platinum-iridium, which is kept at the BIPM under conditions specified by the 1st CGPM in 1889. ... The hertz (symbol Hz) is the SI unit of frequency. ... The metre (American spelling: meter), symbol: m, is the basic unit of distance (or of length, in the parlance of the physical sciences) in the International System of Units. ...

It is simple to see why we perceive a continuum of energy in the correspondence limit. With = 1Hz, the difference between each energy level is J, well below what we can detect. The joule (symbol J, also called newton metre, or coulomb volt) is the SI unit of energy and work. ...

Quote

Every theory is killed sooner or later... But if the theory has good in it, that good is embodied and continued in the next theory. —Albert Einstein Portrait of Albert Einstein taken by Yousuf Karsh on February 11, 1948 Albert Einstein (March 14, 1879 – April 18, 1955) was a theoretical physicist who is widely regarded as the greatest scientist of the 20th century. ...

References

• Weidner, Richard T., and Sells, Robert L. (1980) Elementary Modern Physics. ISBN 0-205-06559-7