| 单词 | quantum mechanics |
| 释义 | quantum mechanics A system of mechanics based on quantum theory, which arose out of the failure of classical mechanics and electromagnetic theory to provide a consistent explanation of both electromagnetic waves and atomic structure. Many phenomena at the atomic level puzzled physicists at the beginning of the 20th century because there seemed to be no way of explaining them without making use of incompatible concepts. One such phenomenon was the emission of electrons from the surface of a metal illuminated by light. Einstein realized that the classical description of light as a wave on an electromagnetic field could not explain this photoelectric effect, as it is called. Experiments showed that electrons would be emitted only if the incident light was of a sufficiently short wavelength, while the intensity of the light appeared not to be relevant. It seemed not to make sense that small ripples of short wavelength could easily knock electrons out of the metal, but a huge tidal wave of long wavelength could not. In 1905 Einstein abandoned classical mechanics and sought an explanation of this photoelectric effect in Planck's work on thermal radiation (see Planck's radiation law). In this work light energy is regarded as being imparted to matter in discrete packets rather than continuously, as one might expect from a wave. Einstein assumed that in the photoelectric effect, light behaves as a shower of particles, each with energy E given by Planck's expression: E = hf ,where f is the light's frequency and h is the Planck constant. Each particle of light, which Einstein called a photon, would impart its energy to a single electron in the metal. The electron would be liberated only if the photon could impart at least the required amount of energy. However many photons were falling on the surface of the metal, no electrons would be liberated unless individual photons had the required energy (hf) to break the attractive forces holding the electrons in the metal. This elegantly quantified reversion to Newton's corpuscular theory of light by Einstein was one of the milestones in the development of quantum mechanics.Further verification that light could indeed behave as a shower of particles came from the Compton effect. In Compton scattering, X-radiation is scattered off an electron in a manner that resembles a particle collision. The momentum imparted to the electron can be predicted by assuming that the X-ray possesses the momentum of a photon. An expression for photon momentum is suggested by the classical theory of radiation pressure. It is known that if energy is transported by an electromagnetic wave at a rate W joules per unit area per second, the wave exerts a radiation pressure W/c, where c is the speed of light. Planck's expression for the energy of photons therefore led to an equivalent expression for the momentum p of these photons: p = h/λ , where λ is the wavelength of the light. Experimental studies of the Compton effect produce results in good agreement with this expression.Both the photoelectric effect and the Compton effect imply that light imparts energy and momentum to matter in the form of packets. It is as if energy and momentum are fundamental ‘currencies’ of physical interaction, and that these currencies exist in denominations that are all multiples of the Planck constant. These quantities are said to be ‘quantized’ and a packet of energy or momentum is called a quantum. Quantum mechanics is essentially concerned with the exchange of these quanta of energy and momentum. For more than a century before the birth of quantum mechanics, experiments had indicated that light behaves as a wave. The successful explanation of the photoelectric and Compton effects demonstrated that in some situations light interacts with matter as if it is a shower of particles. The principle that two models are required to explain the nature of light was called by Niels Bohr complementarity. This principle was extended by the French aristocrat, Louis de Broglie, who suggested that particles of matter might also behave as waves in certain circumstances. Louis de Broglie received the Nobel Prize for this idea in 1929 after the successful measurement of the de Broglie wavelength of an electron in 1927 by Clinton Davisson and Lester Germer, who had observed the diffraction of electrons by single crystals of nickel. The behaviour of individual electrons seemed random and unpredictable, but when a large number had passed through the crystal a typical diffraction pattern emerged. This provided proof that the electron, which until then had been thought of simply as a particle of matter, could under the right circumstances exhibit wavelike properties. Classical mechanics and electromagnetism were based on two kinds of entity: matter and fields. In classical physics, matter consists of particles and waves are oscillations on a field. Quantum mechanics blurs the distinction between matter and field. Modern physicists are forced to concede that the universe is made up of entities that exhibit a wave—particle duality. A new representation of matter and field is needed to fully appreciate this wave—particle duality. In quantum mechanics, an electron is represented by a complex number called a wave function that depends on time and space coordinates. The wave function behaves like a classical wave displacement on a medium (e.g. on a string), exhibiting wave behaviour, interference, diffraction, etc. However, unlike a classical wave displacement, the wave function is essentially a complex quantity. Since an electron's observable properties do not involve complex numbers, it follows that an electron's wave function cannot itself be identified with a single physical property of the electron. The diffraction of electrons observed by Davisson and Germer revealed that, although the behaviour of the individual electrons is random and unpredictable, when a large number have passed through the apparatus, a diffraction pattern is formed whose intensity distribution is proportional to the intensity of the associated wave function. The intensity of the wave function, Ψ, is the square of its absolute value |ψ|2. Therefore, although an electron's wave function itself has no physical significance, the square of its absolute value at a point turns out to be proportional to the probability of finding an electron at that point. The electron wave function must satisfy a wave equation based on the conservation of energy and momentum for the electron. There are two main ways of treating this wave equation: a classical or a relativistic treatment. The resulting wave equations are called eigenvalue equations because they have the same form as equations in a branch of mathematics called eigenvalue problems , i.e. ωΨ= ωΨ ,where ω is some mathematical operation (multiplication by some number, differentiation, etc.) on the wave function Ψ and ω, called the eigenvalue in quantum mechanics, is always a real number. In such an equation the wave function is often called the eigen function . This form of treatment of quantum mechanics is known as wave mechanics (see also Schrödinger equation).The energy E and momentum p of an electron are associated with the frequency f and wavelength λ of the electron's wave using the expressions E = hf and p = h/λ . While the wave equation expresses the behaviour of the wavelike properties of a particle, it does not define the physical attributes it has as a particle. As a particle, the electron has an easily defined spatial and temporal position, not possessed by an oscillation of some kind of field, whose influence extends over a region of space and time. The incompatibility of these two views of the electron leads to the Heisenberg uncertainty principle. Heisenberg recognized that if matter had wavelike properties, the physical attributes normally associated with matter (position, momentum, kinetic energy, etc.) would have to be expressed in a statistical, rather than a deterministic, manner. This is illustrated by the electron diffraction patterns of Davisson and Germer. Individual electrons somehow fell onto the apparatus to form a pattern statistically consistent with the intensity of a wave function. It is as if the final wave function were made up of a superposition of all the possible positions that the electrons could fall onto, the waves of electrons constructively and destructively interfering to form the final diffraction pattern.It is known that a clever superposition of waves of different wavelengths can lead to a construction of a wave packet of finite extension (see Fourier analysis). However, to produce a packet that exists at a point of zero width requires an infinite number of waves to superimpose. Heisenberg realized that these packets of waves must account for the way in which matter particles, such as electrons, could retain some semblance of their particle-like qualities. However, this must also mean that there is an inherent uncertainty in position and momentum associated with electrons and indeed all particles of matter (see uncertainty principle). Since waves of different wavelength correspond to different possible momentum values of an electron, a superposition of such waves to form a particle at a point would correspond to an infinite uncertainty in the momentum of the electron. Therefore the more one knows about the position of an electron the less one will know about its momentum and vice versa. A similar uncertainty between the energy of the electron and its temporal position also exists. Quantities that are related by such an uncertainty principle are said to be incompatible . An alternative to the wave mechanical treatment of quantum mechanics is an equivalent formalism called matrix mechanics, which is based on mathematical operators. See also Bell's theorem; hidden-variables theory |
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