Quantum mechanics is a branch of physics that studies the laws of motion of microscopic particles. It mainly studies the basic theory of the structure and properties of atoms, molecules, condensed matter, nuclei and elementary particles. Together with the theory of relativity, it forms the theoretical basis of modern physics. Quantum mechanics is not only one of the basic theories of modern physics, but also widely used in chemistry and many modern technologies.
Some people cite randomness in quantum mechanics to support the theory of free will, but first, there is still an insurmountable distance between this randomness on the micro scale and macro free will in the usual sense; Secondly, it is difficult to prove whether this randomness is irreducible, because people's observation ability on the micro scale is still limited. Whether nature is really random is still an open question. Many examples of random events in statistics are strictly decisive.
A brief history of the development of quantum mechanics
Quantum mechanics is developed on the basis of the old quantum theory. The old quantum theory includes Planck's quantum hypothesis, Einstein's light quantum theory and Bohr's atomism.
1900, Planck put forward the radiation quantum hypothesis, assuming that the energy exchange between electromagnetic field and matter is realized in a discontinuous form (energy quantum), and the size of the energy quantum is proportional to the radiation frequency, and the proportional constant is called Planck constant, thus obtaining the energy distribution formula of blackbody radiation and successfully explaining the blackbody radiation phenomenon.
1905, Einstein introduced the concept of photon, gave the relationship between the energy and momentum of photon and the frequency and wavelength of radiation, and successfully explained the photoelectric effect. Later, he proposed that the vibration energy of solids is also quantized, thus explaining the specific heat of solids at low temperatures.
19 13, Bohr established the quantum theory of atoms on the basis of Rutherford's nuclear atom model. According to this theory, electrons in atoms can only move in discrete orbits, and atoms have definite energy. This state is called "steady state", and atoms can only absorb or radiate energy from one steady state to another. Although this theory has many successes, there are still many difficulties in further explaining the experimental phenomena.
After people realized that light has the duality of fluctuation and particles, in order to explain some phenomena that cannot be explained by classical theory, French physicist De Broglie put forward the concept of matter wave in 1923. People think that all microscopic particles are accompanied by a wave, which is called de Broglie wave.
De Broglie's equation of matter wave: E=? Ω, p=h/λ, where? = h/2π, which can be expressed by E=p? /2m gives λ = √ (h? /2mE).
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. When the particle size changes from micro to macro, the law it follows also changes from quantum mechanics to classical mechanics.
The difference between quantum mechanics and classical mechanics lies in the description of the state of particles, mechanical quantities and their changing laws. In quantum mechanics, the state of particles is described by wave function, which is a complex function of coordinates and time. In order to describe the law of microscopic particle state changing with time, it is necessary to find out the motion equation satisfied by wave function. This equation was first discovered by Schrodinger in 1926, and it is called Schrodinger equation.
When microscopic particles are in a certain state, their mechanical quantities (such as coordinates, momentum, angular momentum, energy, etc. Generally, there are a series of possible values, and each possible value appears with a certain probability. When the state of the particle is determined, the probability that the mechanical quantity has a certain possible value is completely determined. This is the uncertainty relation obtained by Heisenberg in 1927. At the same time, Bohr put forward the principle of union, which further explained quantum mechanics.
The combination of quantum mechanics and special relativity produces relativistic quantum mechanics. Quantum electrodynamics was developed through the work of Dirac, Heisenberg (also known as Heisenberg, the same below) and Pauli. Quantum field theory, which describes various particle fields, has been formed since 1930s, and it forms the theoretical basis for describing basic particle phenomena.
Quantum mechanics was developed and established after the establishment of the old quantum theory. In order to explain some phenomena in the microscopic field, the old quantum theory artificially revised or attached some conditions to the classical physical theory. Because the old quantum theory is not satisfactory, people have established quantum mechanics from two different paths when looking for the laws in the microscopic field.
1925, Heisenberg only dealt with the knowledge of observable measurement based on physical theory, abandoned the concept of unobservable orbit, and established matrix mechanics based on observable radiation frequency and intensity with Born and Iordan. 1926, Schrodinger found the equation of motion of the micro-system based on the knowledge that quantum is the reflection of the fluctuation of the micro-system, thus establishing wave mechanics, and proved the mathematical equivalence between wave mechanics and matrix mechanics shortly thereafter; Dirac and Iordan independently developed a universal transformation theory and gave a concise and perfect mathematical expression of quantum mechanics.
Heisenberg also put forward the uncertainty principle, the formula of which is as follows: Δ x Δ p ≥/2.
Basic contents of quantum mechanics
The basic principles of quantum mechanics include the concept of quantum state, the corresponding rules and physical principles between motion equations, theoretical concepts and observed physical quantities.
In quantum mechanics, the state of a physical system is represented by state functions, and the arbitrary linear superposition of state functions still represents a possible state of the system. The change of state with time follows a linear differential equation, which predicts the behavior of the system. Physical quantities are represented by operators that meet certain conditions and represent some operation. The operation of measuring the physical quantity of a physical system in a certain state corresponds to the effect of the operator representing the quantity on its state function; The possible value of measurement is determined by the eigenequation of the operator, and the expected value of measurement is calculated by the integral equation containing the operator.
The square of the state function represents the probability that a physical quantity is its variable. According to these basic principles and other necessary assumptions, quantum mechanics can explain various phenomena of atoms and subatomics.
According to Dirac symbol, the state function is expressed by and the probability density of the state function is expressed by ρ =
The state function can be expressed as a state vector expanded in an orthogonal space set, such as | ψ (x) >; =∑|ρ_ I & gt； , where | ρ _ i > Is a space basis vector orthogonal to each other, < m | n & gt=δm, and n is a Dirac function, which satisfies the orthogonal normalization property.
The state function satisfies Schrodinger wave equation, I? (d/dt)| m & gt； = H | m> After the variables are separated, the temporal evolution equation H | m > can be obtained. = En | m>, En is the energy eigenvalue and h is the Hamiltonian energy operator.
Therefore, the quantization of classical physical quantities comes down to the solution of Schrodinger wave equation.
The explanation of quantum mechanics involves many philosophical problems, the core of which is causality and physical reality. According to the causality in the sense of dynamics, the motion equation of quantum mechanics is also the causality equation. When the state of the system at a certain moment is known, its future and past state at any moment can be predicted according to the equation of motion.
However, the prediction of quantum mechanics is essentially different from that of classical physical equations of motion (particle motion equation and wave equation). In the classical physics theory, the measurement of a system will not change its state, but it only changes and evolves according to the equation of motion. Therefore, the equation of motion can clearly predict the mechanical quantities that determine the state of the system.
But in quantum mechanics, there are two changes in the state of the system. One is that the state of the system evolves according to the equation of motion, which is a reversible change; The other is to measure irreversible changes that change the state of the system. Therefore, quantum mechanics can not give a definite prediction about the physical quantity that determines the state, but can only give the probability of taking the value of the physical quantity. In this sense, the causal law of classical physics has failed in the microscopic field.
Based on this, some physicists and philosophers assert that quantum mechanics abandons the law of causality, while others believe that the law of causality of quantum mechanics reflects a new law of causality-probabilistic causality. In quantum mechanics, the wave function representing the quantum state is defined in the whole space, and the change of any state is realized in the whole space at the same time.
Since the 1970s, experiments on the correlation of distant particles have shown that space-like separation events are related to the predictions of quantum mechanics. This correlation contradicts the view of special relativity, which holds that the physical interaction between objects can only propagate at a speed not greater than the speed of light. Therefore, in order to explain the existence of this correlation, some physicists and philosophers have proposed that there is a global causality or global causality in the quantum world, which is different from the local causality based on special relativity and can determine the behavior of related systems as a whole.
Quantum mechanics uses the concept of quantum state to represent the state of microscopic system, which deepens people's understanding of physical reality. The properties of microscopic systems are always shown in the interaction with other systems, especially observation instruments.
When people describe the observation results in the language of classical physics, it is found that the microscopic system is mainly characterized by fluctuating images or particle behaviors under different conditions. The concept of quantum state expresses the possibility of waves or particles generated by the interaction between microscopic systems and instruments.
Quantum mechanics shows that micro-physical reality is neither wave nor particle, and the real reality is quantum state. The decomposition of real state into hidden state and explicit state is caused by measurement, and only explicit state here conforms to the meaning of classical physical real. The reality of micro-system is also reflected in its inseparability. Quantum mechanics regards the research object and its environment as a whole, and it is not allowed to regard the world as composed of separate and independent parts. The experimental results of long-distance particle correlation also quantitatively support the inseparability of quantum States. Uncertainty means that economic actors can't know the result of their own decisions accurately in advance. In other words, as long as the decision of economic actors has more than one possible outcome, uncertainty will arise.
Uncertainty also refers to the uncertainty of quantum motion in quantum mechanics. Because the observation interferes with some quantities, the quantity associated with it (* * * yoke quantity) is inaccurate. This is the source of uncertainty.
Uncertainty, the concept of risk management in economics, means that economic subjects cannot know the distribution range and state of future economic conditions (especially gains and losses).
In quantum mechanics, uncertainty refers to the uncertainty of measuring physical quantities, because under certain conditions, some mechanical quantities can only be in their eigenstates, and the displayed values are discrete, so it is possible to get different values at different times, and there will be uncertain values, that is, when you measure, you may get this value or that value, and the obtained values are uncertain. Only by measuring the eigenstate of this mechanical quantity can we get an accurate value.
In classical physics, the position and momentum of a particle can be used to accurately describe its motion. At the same time, knowing the acceleration, we can even predict the position and momentum of the particle at any time in the future, thus drawing the trajectory. But in microphysics, uncertainty tells us that if we want to measure the position of particles more accurately, the measured momentum will be more inaccurate. In other words, it is impossible to accurately measure the position and momentum of a particle at the same time, so it is impossible to describe the motion of a particle by trajectory. This is the concrete explanation of the uncertainty principle.
bohr
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Bohr, an outstanding contributor to quantum mechanics, pointed out the concept of electron orbital quantization. Bohr thinks that the nucleus has a certain energy level. When an atom absorbs energy, it is in an excited state. When an atom releases energy, it jumps to the ground state. Whether the atomic energy level jumps depends on the difference between the two energy levels. According to this theory, Rydberg's common sense can be calculated theoretically, which is in good agreement with the experiment. But Bohr's theory also has limitations. For larger atoms, the error of calculation results is very large. Bohr still retains the concept of orbit in the macro world. In fact, the coordinates of electrons appearing in space are uncertain, and there are many electrons gathered, which shows that the probability of electrons appearing here is high, and vice versa. Many electrons gather together, which can be called an electron cloud.
The birth of quantum mechanics
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19 At the end of the 20th century, classical physics had developed to a fairly perfect level, but some serious difficulties were encountered in the experiment. These difficulties are regarded as "a few dark clouds in the clear sky", and it is these dark clouds that have triggered the changes in physics. Several difficulties are briefly described as follows:
(1) blackbody radiation problem
When the complete black body (empty pit) is in balance with thermal radiation, the radiation energy density changes with frequency in a curve. W.Wien got a semi-classical formula from the general theory of thermodynamics and the analysis of experimental data. Most of the formulas are in good agreement with the experimental curves, but in the long wave band, the formulas obviously deviate from the experiments. This prompted Planck to improve Wayne formula and get a Planck formula with two parameters, which is in good agreement with the experimental data.
⑵ photoelectric effect
Due to ultraviolet radiation, a large number of electrons escape from the metal surface. Through research, it is found that the photoelectric effect has the following characteristics:
A has a certain critical frequency. Only when the frequency of incident light is greater than the critical frequency, photoelectrons will escape.
The energy of each photoelectron is only related to the frequency of the irradiated light.
C. When the frequency of incident light is greater than the critical frequency, photoelectrons can be observed almost immediately as soon as the light is irradiated.
Among the above three characteristics, C is a quantitative problem, while A and B cannot be explained by classical physics in principle.
⑶ Linear spectrum of atoms and its laws
Spectral analysis has accumulated a wealth of data, which many scientists have sorted out and analyzed, and found that atomic spectrum is a discrete linear spectrum rather than a continuous distribution. The wavelength of spectral lines also has a very simple law.
(4) the stability of atoms
After the discovery of Rutherford model, according to classical electrodynamics, the accelerated charged particles will continue to radiate and lose energy. Therefore, electrons moving around the nucleus will eventually' fall' into the nucleus due to a large loss of energy. So atoms will collapse. But the real world shows that atoms are stable.
5] Specific heat of solids and molecules
When the temperature is very low, the equal energy theorem does not apply.
Planck-Einstein Optical Quantum Theory
Quantum theory is the first breakthrough to the problem of blackbody radiation. Planck put forward the concept of quantum -h in order to deduce his formula theoretically, but it did not attract many people's attention at that time. Einstein put forward the concept of light quantum by using quantum hypothesis, thus solving the problem of photoelectric effect. Einstein further applied the concept of energy discontinuity to the vibration of atoms in solids, and successfully solved the phenomenon that the specific heat of solids tends to zero at T→0K. The concept of light quantum has been directly verified in Compton scattering experiment.
Bohr's quantum theory
Bohr creatively applied Planck-Einstein concept to solve the problems of atomic structure and atomic spectrum, and put forward his atomic quantum theory. It mainly includes two aspects:
A. Atomic energy can only exist stably in a series of states corresponding to discrete energy. These states become stable.
When an atom transitions between two steady states, the frequency v of absorption or emission is unique and given by hv=En-Em. Bohr's theory achieved great success, which opened the door for people to understand the atomic structure for the first time, and its existing problems and limitations were gradually discovered by people.
De Broglie matter wave
Inspired by Planck and Einstein's light quantum theory and Bohr's atomic quantum theory, considering that light has wave-particle duality, De Broglie assumes that real physicists also have wave-particle duality according to the analogy principle. He put forward this hypothesis, on the one hand, in an attempt to unify physical particles with light, on the other hand, in order to understand the discontinuity of energy more naturally, so as to overcome the shortcomings of Bohr's artificial quantization conditions. In the electron diffraction experiment of 1927, the direct proof of physical particle fluctuation is realized.
The establishment of quantum mechanics
Quantum mechanics itself was established in the period of 1923- 1927. Almost at the same time, two equivalent theories-matrix mechanics and wave mechanics were put forward. The introduction of matrix mechanics is closely related to Bohr's early quantum theory. On the one hand, Heisenberg inherited the reasonable concepts in early quantum theory, such as energy quantization, steady state and transition, and abandoned some concepts without experimental basis, such as electron orbit. The matrix mechanics of Heisenberg, Born and Jordan can be measured physically, and each physical quantity is given a matrix. Their algebraic operation rules are different from classical physical quantities and obey algebra which is not easy to multiply. Wave mechanics comes from the idea of matter waves. Inspired by matter wave, Schrodinger discovered a motion equation of matter wave in quantum system-Schrodinger equation, which is the core of wave mechanics. Later, Schrodinger also proved that matrix mechanics and wave mechanics are completely equivalent and are two different forms of the same mechanical law. In fact, quantum theory can be expressed more generally, which is the work of Dirac and Jordan.
The establishment of quantum physics is the result of the cooperation of many physicists Qi Xin, which marks the first collective victory of physics research.
The emergence and development of quantum mechanics
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Quantum mechanics is a physical science that describes the structure, movement and changing laws of the micro-world. This is a great leap in the development of human civilization in the 20th century. The discovery of quantum mechanics has triggered a series of epoch-making scientific discoveries and technological inventions, and made important contributions to the progress of human society.
At the end of 19, when people made great achievements in classical physics, a series of phenomena that could not be explained by classical theory were discovered one after another. The thermal radiation theorem discovered by German physicist Wayne by measuring the thermal radiation spectrum. German physicist Planck put forward a bold hypothesis to explain the energy spectrum of thermal radiation: in the process of generation and absorption of thermal radiation, energy exchange is carried out with hV as the minimum unit. This assumption of energy quantization not only emphasizes the discontinuity of thermal radiation energy, but also directly contradicts the basic concept that radiation energy and frequency are independent and determined by amplitude, which cannot be included in any classical category. At that time, only a few scientists studied the problem seriously.
Einstein, a famous scientist, put forward the theory of light quantum in 1905 after careful consideration. 19 16 American physicist Millikan published the experimental results of photoelectric effect, which verified Einstein's optical quantum theory.
19 13 years, Danish physicist Bohr put forward the steady-state hypothesis, which solved the instability of Rutherford's atomic planetary model (according to classical theory, electrons in atoms move around the nucleus and radiate energy, resulting in a decrease in orbital radius until they fall into the nucleus and are positively charged): electrons in atoms cannot move in any classical mechanical orbit like planets, and the amount of action to stabilize the orbit must be an integer multiple of H (quantization of angular momentum) The frequency of light is determined by the energy difference AE = HV between orbital States, that is, the frequency law. In this way, Bohr's atomic theory explained the discrete spectral lines of hydrogen atoms with simple and clear images, and intuitively explained the periodic table of chemical elements with electronic orbital states, which led to the discovery of lead 72 and triggered a series of important scientific progress in the following ten years. This is unprecedented in the history of physics.
Due to the profound connotation of quantum theory, the Copenhagen School, represented by Bohr, has conducted in-depth research on it. They have studied correspondence principle, matrix mechanics, incompatibility principle, uncertainty relation and complementarity principle. The probability interpretation of quantum mechanics has made contributions.
1923 In April, American physicist Compton published the phenomenon that the frequency of X-rays is reduced due to electron scattering, that is, Compton effect. According to the classical wave theory, the scattering of waves by stationary objects will not change the frequency. According to Einstein's quantum of light, this is the result of the collision of two "particles". When light quantum collides, it not only transfers energy, but also transfers momentum to electrons, which proves the theory of light quantum by experiments.
Light is not only an electromagnetic wave, but also a particle with energy momentum. 1924, American Austrian physicist Pauli published the "incompatibility principle": no two electrons in an atom can be in the same quantum state at the same time. This principle explains the shell structure of electrons in atoms. This principle applies to all elementary particles of solid matter (usually called fermions, such as protons, neutrons, quarks, etc. ), which constitutes the basic point of quantum statistical mechanics-Fermi statistics. In order to explain the fine structure of spectral lines and the anomalous Zeeman effect, Pauli suggested that in addition to the three existing quantum numbers corresponding to classical mechanical quantities (energy, angular momentum and its components), a fourth quantum number should be introduced into the original electron orbital state. This quantum number, later called "spin", is a physical quantity that expresses an intrinsic property of elementary particles.
1924, the French physicist de Broglie put forward the Einstein-de Broglie relation to express wave-particle duality: e = HV, p = h/in, and the energy and momentum of physical quantities representing particle properties are equal to the frequency and wavelength representing wave properties through a constant h.
1925, German physicists Heisenberg and Bohr,