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Wave-particle duality means that a substance has both wave characteristics and particle characteristics. Wave-particle duality is an important concept in quantum mechanics.
Wave-particle duality means that a substance has both wave characteristics and particle characteristics. Wave-particle duality is an important concept in quantum mechanics. In classical mechanics, the research objects are always clearly divided into two categories: waves and particles. The typical example of the former is light, while the latter constitutes what people often call "matter". 1905, Einstein put forward the optical quantum explanation of photoelectric effect, and people began to realize that light waves have both the properties of waves and particles. 1924, de Broglie put forward the "material wave" hypothesis, which holds that all matter, like light, has wave-particle duality. According to this hypothesis, electrons will also have fluctuations such as interference and diffraction, which was confirmed by later electron diffraction experiments.
Wave-particle duality-mathematical relationship
The Mathematical Relationship between "Wave" and "Particle"
The particle nature of matter is characterized by energy e and momentum p, while the characteristics of wave are represented by electromagnetic wave frequency ν and its wavelength λ. The scaling factors of these two groups of physical quantities are related by Planck constant h (h = 6.626 * 10-34J s).
E = HV and E = MC 2 are simultaneous, and we get: M = HV/C 2 (this is the relativistic mass of photons, so photons have no rest mass because they can't rest) and p=mc, then p=hv/c(p is momentum).
Wave-particle duality-historical introduction
Wave-particle duality1In the late 9th century, the increasingly mature atomism gradually prevailed. According to the atomic theory, all matter is made up of tiny particles-atoms. For example, electricity, which was originally considered as a fluid, was proved by Thompson's cathode ray experiment to be composed of particles called electrons. Therefore, people think that most substances are composed of particles. At the same time, wave is considered as another way of existence of matter. The wave theory is deeply studied, including interference and diffraction. Because of the characteristics of light in Thomas Young double-slit interference experiment and Fraunhofer diffraction, it is obvious that it is a fluctuation.
However, at the beginning of the twentieth century, this view faced some challenges. The photoelectric effect studied by Albert Einstein in 1905 shows the particle surface of light. Subsequently, the electron diffraction was predicted and confirmed. This shows the fluctuating side of electrons that were originally thought to be particles. This wave-particle mystery was finally solved by the establishment of quantum mechanics in the early twentieth century, which is called wave-particle duality. It provides a theoretical framework, so that any substance can show these two characteristics in a specific environment. Quantum mechanics holds that all particles in nature, such as photons, electrons or atoms, can be described by a differential equation, such as Schrodinger equation. The solution of this equation is the wave function, which describes the state of particles. Wave functions are superimposed, that is, they can interfere and diffract each other like waves. At the same time, the wave function is also interpreted as describing the probability amplitude of particles appearing in a specific position. In this way, particles and waves are unified in the same explanation.
The reason why the fluctuation of objects can't be observed in daily life is that their mass is too large, which leads to the characteristic wave being less than the observable limit in the long run, so the scale of possible fluctuation is beyond the scope of daily life experience. This is why classical mechanics can satisfactorily explain "natural phenomena". On the contrary, for elementary particles, their mass and scale determine that their behavior is mainly described by quantum mechanics, which is far from what we are used to.
Wave-particle duality-early light theory
Huygens and Newton's Early Light Theory
The earliest comprehensive light theory of wave-particle duality was put forward by christiaan huygens, who put forward the wave theory of light, explaining how light waves form wave fronts and propagate along straight lines. This theory can also explain the refraction phenomenon well. However, the theory encountered difficulties in other aspects. So it was soon surpassed by isaac newton's particle theory. Newton thought that light was composed of tiny particles, so that he could naturally explain the phenomenon of reflection. Moreover, he can explain the refraction phenomenon of the lens with a little effort, and break the sunlight into rainbows through the prism.
Because of Newton's unparalleled academic position, no one dared to challenge his theory for more than a century, and Huygens' theory was gradually forgotten. It was not until the diffraction phenomenon was discovered at the beginning of19th century that the wave theory of light was re-recognized. However, the debate between the fluctuation and particle nature of light has never subsided.
The Theories of Fenier, Maxwell and Yang Guang
/kloc-The double-slit interference experiment demonstrated by Thomas Young, Augustine and Jean Venier at the beginning of the 9th century provided the experimental basis for Huygens' theory. These experiments show that interference patterns can be observed when light passes through the grid, which is very similar to the interference behavior of water waves. Moreover, the wavelength of light can be calculated from these patterns. James clerk maxwell gave a set of equations at the end of the century, which revealed the properties of electromagnetic waves. The result of the equation is that the propagation speed of electromagnetic waves is the speed of light, which makes light widely accepted as an explanation of electromagnetic waves, and Huygens' theory has been re-recognized.
Einstein and Photons
Wave-particle duality 1905, Einstein put forward the theory of photoelectric effect, which solved the experimental phenomenon that the previous wave theory of light could not explain. He introduced the concept of photon, which is a quantum that carries light energy. In the photoelectric effect, it is observed that a beam of light shining on some metals will produce a certain current in the circuit. It can be inferred that light knocks out electrons in metal and makes it flow. But at the same time, it has been observed that for some materials, even a faint blue light can generate current, but no matter how strong the red light is, it can't draw current from it. According to wave theory, the intensity of light corresponds to the energy it carries, so strong light can certainly provide stronger energy to knock out electrons. However, the fact is just the opposite.
Einstein explained it as quantization effect: electrons are knocked out of metal by photons, and each photon has a part of energy E, which corresponds to the frequency ν of light ν: E = H ν, where h is Planck constant (6.626 x 10-34JS). The color of a light beam depends on the frequency of photons, while the light intensity depends on the number of photons. Due to the quantization effect, each electron can only accept the energy of photons as a whole, so only high-frequency photons (blue light, not red light) have the ability to knock out electrons. Einstein won the 192 1 Nobel Prize in Physics for his theory of photoelectric effect.
Photoelectric effect equation
Because E=hv, this light shines on the atom, in which electrons absorb some energy, thus overcoming the work function and escaping from the atom. The kinetic energy of an electron Ek=hv-W, where W is the work function required for an electron to escape from an atom. This is Einstein's photoelectric effect equation.
Wave-Particle Duality —— De Broglie Hypothesis
Wave-particle duality 1924, Louis Victor? De? Broglie noticed that the stable motion of electrons in atoms needs to be described by introducing integers, which is similar to other phenomena involving integers in physics, such as interference and vibration normal modes. He constructed the De Broglie hypothesis and proposed that physical particles also have wave-particle duality just as light has wave-particle duality. He related the wavelength λ to the momentum p and got λ = h/p.
This is a generalization of Einstein's equation, because the momentum of photons is p=E/c(c is the speed of light in vacuum) and λ = c/v. De Broglie equation is proved by two independent electron scattering experiments on electrons (with rest mass). ClintonJosephDavisson and LesterHalbertGermer of Bell Laboratories used low-speed electron beams to irradiate nickel single crystals. The electron is diffracted by single crystal, and the measured electron wavelength accords with de Broglie formula. At the University of Aberdeen, GeorgePagetThomson obtained a diffraction pattern similar to that produced by X-rays on polycrystalline metal foil of high-speed electrons, which definitely confirmed the fluctuation of electrons. Later, other experiments observed the diffraction phenomena of helium atoms, hydrogen molecules and neutrons, and the fluctuation of microscopic particles was widely confirmed. The electron microscope, electron diffraction technology and neutron diffraction technology developed according to the fluctuation of microscopic particles have become powerful means to detect the microstructure and crystal structure analysis of substances.
De Broglie won the 1929 Nobel Prize in Physics for this hypothesis. Thomson and Davisson won the 1937 Nobel Prize in Physics for their experimental work. How to unify the wave-particle duality of light and microscopic particles is the most puzzling problem in the history of human cognition, and it cannot be said that the problem has been completely solved so far. 1926, M Born put forward the explanation of probability wave, which solved this problem well. According to the explanation of probability wave, the wave function ψ (x, y, z, t) used to describe particle fluctuation is a probability wave, not a concrete matter wave. The square of the absolute value of wave function | ψ| 2 =ψ * ψ represents the probability density of particles appearing in X, Y and Z at time t, and ψ * represents the * * yoke wave function of ψ. In the interference experiment of electrons passing through two holes, | ψ | 2 =|ψ1+ψ 2 | 2 = |ψ1| 2+| ψ 2 | 2+ψ1* ψ 2. ψ 1 * ψ 2+ψ 1 ψ 2 * is a term reflecting the interference effect. No matter under the condition of high particle current intensity or weak particle current, the results of interference fringes are the same if the particles are patted one by one and repeated many times.
The interference effect shown in repeated experiments in which the particle flow is weak and the particles are injected one by one shows that the fluctuation of microscopic particles is not the nature of a large number of particles gathering, but a single particle has fluctuation. So on the one hand, the particles are inseparable, on the other hand, in the double-hole experiment, the two holes work at the same time. Therefore, it is meaningless to talk about the trajectory of microscopic particles. Because microscopic particles have wave-particle duality, they follow different motion laws from macroscopic objects, and quantum mechanics describing the motion laws of microscopic particles is also different from classical mechanics describing the motion laws of macroscopic objects.
Schrodinger equation
Solving particle problems in wave-particle duality quantum mechanics often boils down to solving Schrodinger equation or stationary Schrodinger equation. Schrodinger equation is widely used in atomic physics, nuclear physics and solid physics, and the results of solving a series of problems such as atoms, molecules, nuclei and solids are in good agreement with reality. Schrodinger equation is only applicable to non-relativistic low-speed particles, and it does not contain a description of particle spin. When the relativistic effect is considered, the Schrodinger equation is replaced by the relativistic quantum mechanical equation, which naturally includes the spin of particles.
The basic equation of quantum mechanics proposed by Schrodinger. Established on 1926. It is a non-relativistic wave equation. It reflects the law describing the state of microscopic particles changing with time, and its position in quantum mechanics is equivalent to Newton's law of classical mechanics, which is one of the basic assumptions of quantum mechanics. Let the wave function describing the state of microscopic particles be ψ (r, t), and the Schrodinger equation of microscopic particles with mass m moving in the potential field U(r, t) is. The wave function ψ (r, t) can be solved under the given initial and boundary conditions and the single-valued, finite and continuous conditions that the wave function satisfies. From this, the distribution probability of particles and the average value (expected value) of any possible experiments can be calculated. When the potential function u does not depend on time t, the particle has definite energy, and the state of the particle is called steady state. The steady-state wave function can be written as a formula, in which ψ (r) is called the steady-state wave function, which satisfies the steady-state Schrodinger equation and is called the eigenvalue equation mathematically, where E is the eigenvalue and the steady-state energy, and ψ (r) is also called the eigenfunction belonging to the eigenvalue E.
Solving particle problems in quantum mechanics often boils down to solving Schrodinger equation or stationary Schrodinger equation. Schrodinger equation is widely used in atomic physics, nuclear physics and solid physics, and the results of solving a series of problems such as atoms, molecules, nuclei and solids are in good agreement with reality. Schrodinger equation is only applicable to non-relativistic low-speed particles, and it does not contain a description of particle spin. When the relativistic effect is considered, the Schrodinger equation is replaced by the relativistic quantum mechanical equation, which naturally includes the spin of particles.