Quantum mechanics is a sub-discipline of physics that studies the motion laws of microscopic particles, which mainly studies the basic theory of the structure and properties of atoms, molecules, condensed matter, atomic nuclei and elementary particles, and it forms the theoretical basis of modern physics together with the theory of relativity.
Quantum mechanics is not only one of the basic theories of modern physics, but also has been widely used in chemistry and other related disciplines 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 microscopic scale and free will at the macroscopic level in the usual sense; Second, it is difficult to prove whether this randomness is irreducible, because people's ability to observe at the microscopic scale is still limited.
Whether nature is truly random is an open question.
Many examples of random events in statistics are, strictly speaking, decisive.
Quantum mechanics was developed on the basis of the old quantum theory.
Old quantum theories include Planck's quantum hypothesis, Einstein's quantum theory of light, and Bohr's atomic theory.
In 1900, Planck proposed the radiation quantum hypothesis, assuming that the electromagnetic field and matter exchange energy are realized in the form of discontinuous energy particles, the size of energy particles is proportional to the radiation frequency, and the proportionality constant is called Planck's constant, so as to obtain the blackbody radiation energy distribution formula, and successfully explain the blackbody radiation phenomenon.
In 1905, Albert Einstein introduced the concept of optical quantum photons and gave the relationship between the energy and momentum of photons and the frequency and wavelength of radiation, successfully explaining the photoelectric effect.
Subsequently, he proposed that the vibrational energy of solids is also quantized, thus explaining the problem of specific heat of solids at low temperatures.
In 1913, Bohr established a quantum theory of atoms based on Rutherford's model of the nuclear atom.
According to this theory, the electrons in an atom can only move in discrete orbits, the atom has a definite energy, and the state it is in is called a "stationary state", and the atom can only absorb or radiate energy from one stationary state to another.
Although this theory has many successes, there are still many difficulties in further explaining the experimental phenomenon.
After people realized that light has the duality of waves and particles, in order to explain some phenomena that cannot be explained by classical theories, the French physicist de Broglie put forward the hypothesis that microscopic particles have wave-particle duality in 1923.
According to de Broglie, just as light has wave-particle duality, the particles of entities such as electrons, atoms, etc., also have this property, that is, they have both particle and wave properties.
This hypothesis was soon confirmed experimentally. de Broglie's wave-particle duality hypothesis: eaass4509291295; w,h,where AASS4509291295; =h2π, which can be defined by eaass4509291su2; 2 get=haass4509291su2; 2。
Due to the wave-particle duality of microscopic particles, the motion laws followed by microscopic particles are different from those of macroscopic objects, and the quantum mechanics that describes the motion laws of microscopic particles is also different from the classical mechanics that describes the motion laws of macroscopic objects.
When the size of a particle transitions from microscopic to macroscopic, the laws it follows also transition from quantum mechanics to classical mechanics.
The difference between quantum mechanics and classical mechanics is first manifested in the description of the state and mechanical quantity of particles and their change laws.
In quantum mechanics, the state of a particle is described by a wave function, which is a complex function of coordinates and time.
In order to describe the law of the state of microscopic particles as a function of time, it is necessary to find the equation of motion satisfied by the wave function.
This equation was first discovered by Schrödinger in 1926 and is known as the Schrödinger equation.
When a microscopic particle is in a certain state, its mechanical quantities such as coordinates, momentum, angular momentum, energy, etc., generally do not have a definite value, but have a series of possible values, each of which appears with a certain probability.
When the state of the particle is determined, the probability that the mechanical quantity will have a certain possible value is also completely determined.
This is the uncertainty relationship that Heisenberg derived in 1927, and at the same time, Bohr proposed the principle of parallel cooperation, which gave a further explanation of quantum mechanics.
The combination of quantum mechanics and special relativity gives rise to relativistic quantum mechanics.
Quantum electrodynamics was developed through the work of Dirac, Heisenberg, and Pauli, among others.
After the 30s of the 20th century, quantum theory quantum field theory was formed to describe various particle fields, which formed the theoretical basis for describing the phenomenon of elementary particles.
Quantum mechanics was developed and established after the establishment of the old quantum theory.
The old quantum theory imposed some artificial modification or conditionality on the classical physical theory in order to explain some phenomena in the microscopic realm.
Since the old quantum theory was unsatisfactory, quantum mechanics was established from two different paths in search of the laws of the microscopic realm.
In 1925, Heisenberg based on the understanding of physical theory that only dealt with observable quantities, abandoned the concept of unobservable orbits, and established matrix mechanics together with Born and Jordan from the observable radiation frequency and its intensity.
In 1926, Schrödinger found the equation of motion of the microscopic system based on the understanding that quantum is a reflection of the wave of the microscopic system, thus establishing wave dynamics, and soon after proved the mathematical equivalence of wave dynamics and matrix mechanics.
Dirac and Jordan independently developed a universal theory of transformation, giving a concise and complete mathematical expression of quantum mechanics.
Heisenberg also proposed the uncertainty principle, which is expressed in the following formula: ΔxΔaass4509291295; 2。
The basic content of quantum mechanics The basic principles of quantum mechanics include the concept of quantum states, the equations of motion, theoretical concepts, and the corresponding rules and physical principles between observed physical quantities.
In quantum mechanics, the state of a physical system is represented by a state function, and an arbitrary linear superposition of state functions still represents one of the possible states of the system.
The change of state over time follows a linear differential equation that predicts the behavior of a system, and the physical quantities are represented by operators that represent certain operations that meet certain conditions; The operation of measuring a physical quantity of a physical system in a certain state corresponds to the effect of the operator representing that quantity on its state function; The possible value of the measurement is determined by the eigenequation of the operator, and the expected value of the measurement is calculated by an integral equation containing the operator.
The square of the state function represents the probability of occurrence of a physical quantity as its variable.
Based on these basic principles and accompanied by other necessary assumptions, quantum mechanics can explain various phenomena of atoms and subatoms.
According to the Dirac symbol, the state function is denoted by tΨ and Ψgt, the probability density of the state function is denoted by =tΨΨgt, and its probability flow density is aass4509291295; 2iΨΨ-ΨΨ denotes that its probability is the spatial integral of the probability density.
The state function can be expressed as the state vector that expands in the orthogonal space set, such as Ψxgt=igt, where igt is the space base vector orthogonal to each other, tngt=δ, and n is the Dirac function, satisfying the orthogonal normalization property.
The state function satisfies the Schrödinger wave equation, iaass4509291295; ddtgthgt, after separating the variables, we can obtain the evolution equation hgt=engt in the non-timeless state, where en is the eigenvalue of the energy, and h is the Hamiltonian energy operator.
Therefore, the quantization problem of classical physical quantities boils down to the problem of solving the Schrödinger wave equation.
The explanation of quantum mechanics involves many philosophical questions, the core of which is the question of causality and physical reality.
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According to the causal law in the dynamic sense, the equation of motion of quantum mechanics is also the equation of causality, and when the state of a certain moment of the system is known, its future and the state of any moment in the past can be predicted according to the equation of motion.
However, the predictions of quantum mechanics are qualitatively different from those of classical physics, the equations of motion, the equations of motion of mass points, and the equations of waves.
In classical physics, the measurement of a system does not change its state, it has only one change and evolves according to the equations of motion.
Therefore, the equations of motion can make definite predictions about the mechanical quantities that determine the state of the system.
However, in quantum mechanics, there are two kinds of 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 cannot give a definite prediction of the physical quantities that determine the state, but only the probability of the value of the physical quantities.
In this sense, the laws of causality in classical physics fail in the microscopic realm.
Accordingly, some physicists and philosophers assert that quantum mechanics discards causality, while others believe that the causal law of quantum mechanics reflects a new type of causality, probabilistic causality.
The wave function that represents the quantum state in quantum mechanics is defined in the whole space, and any change in the state is realized in the whole space at the same time.
Since the 70s of the 20th century, experiments on the correlation of distant particles have shown that the events of space-like separation are related to those predicted by quantum mechanics.
This correlation contradicts the special theory of relativity, which states that physical interactions between objects can only be transmitted at speeds no greater than the speed of light.
Therefore, some physicists and philosophers have proposed that there is a kind of global causality or global causality in the quantum world, which is different from local causality based on special relativity, and can determine the behavior of related systems as a whole.
Quantum mechanics uses the concept of quantum states to characterize the state of microscopic systems, deepening people's understanding of physical reality.
The nature of microscopic systems is always manifested in their interaction with other systems, especially observation instruments.
When people describe the observations in the language of classical physics, they find that the microscopic system is mainly manifested as a wave image or mainly as a particle behavior under different conditions.
The concept of quantum states, on the other hand, expresses the possibility of microscopic systems interacting with instruments to manifest themselves as waves or particles.
Quantum mechanics shows that microscopic physics is neither a wave nor a particle, but a quantum state.
The decomposition of the real state into the implicit and explicit states is due to measurements, and here only the explicit states correspond to the meaning of the reality of classical physics.
The reality of the microsystem is also manifested in its inseparability.
Quantum mechanics treats the object of study and its environment as a whole, and it does not allow the world to be seen as made up of separate, independent parts.
The conclusions of the distant particle correlation experiment also quantitatively support the inseparability of quantum states: