How to understand that the generalized coordinate number of the Rass function is not equal to the ge

From the time of the first quantization of quantum mechanics, it already contained all subsequent orders of quantization. With one quantization there will be two times, and with two times there will be three times. As the saying goes, the Tao begets one, one begets two, two begets three, and three begets all things.

Therefore, quantum mechanics is in principle a theory of infinite quantization, and there is no longer any certainty in such a theory, because any first-order wave function will be tokenized in the next quantization. The essence of the world should be indeterministic, and the ultimate physics should be a complete loss of certainty! So why are we still so busy calculating wave functions in a quantum framework all day long?

Because, this is a reasonable approximation. It has been recognized in many field-theoretic models that the higher the dimensionality of a quantum field, the weaker the effect of quantum fluctuations. Each time it is quantized, the dimension of the field is increased by an aleph number.

So soon, the quantum fluctuations will be weakened, so we can make a classical approximation. That is, at a certain time of quantization, a truncation is made, and the field operator is replaced by a wave function. In this way, we have the primary or secondary quantization that we commonly use.

Quantization is a process of loss of certainty. In a single quantization, the certainty of all physical quantities is lost. Formally, it means that the physical quantity changes from a definite number to an indefinite operator.

But it doesn't make sense for an operator to hang in the air and swing around. The operator only gains meaning when it is implemented on the wave function. Therefore, the introduction of the wave function is obvious and necessary for a quantization.

The wave function is a function of the state of a particle, and its value is a complex number, and its modulus represents the probability that the particle will appear in that state. Since then, all physical quantities are distributed according to probability, and we can no longer ask "how big is the energy", but only "what is the probability that the energy is so big". But a quantum is not a complete revolution.

There are two physical quantities that are still definite and can be measured: one is the probability itself, and the other is the amount acting as a phase. Together, they can construct the wave function.

Since all physical quantities are uncertain, why is only the probability distribution still determined? Why can't probability distributions also follow probability distributions? Therefore, quadratic quantization is to continue this revolution, to carry out the uncertainty to the end, to deprive the wave function of the certainty, to make the wave function operator, and to make it a field operator.

But the field operator itself is also meaningless, because no operator can exist independently, and the field operator must eventually be implemented into an object. But that's not a wave function, because the field operator itself represents a wave function, so the field operator should act on a more advanced wave function, which is the wave functional. The wave functional is a mapping from the Hilbert space to a field of complex numbers, [mapping each classical configuration (x) (i.e., the wave function) of the field onto a complex number.]

This complex number describes the magnitude of the probability of the occurrence of the wave function of (x), and is therefore the probability of probability. All wave functionals make up a larger "Hilbert space". Based on this construction, we can also implement the third quantization, which is to quantize the wave functional and re-regular into a functional field operator.

In this way, these field operators also need to be implemented. They act on "wave generals". And so recursively, it can be endless.

There are many types of quantum field theory. Generally speaking, we introduce the method of field theory. And the rest is up to you what you're going to do.

Students in condensed matter need non-relativistic fields, so non-relativistic field theory ms is also called quantum multi-kick, right? And the rest is the relativistic field theory, which is what LSS is more concerned about, haha, as for quadratic quantization? I don't agree that what is most needed is the quantization method, and there are many quantization methods.

For example, regular quantization path integral quantization, but in fact, regular quantization needs to start in quantum field theory?..So let's take a look at Cohen's book, in fact, if you don't use regular quantization, how do you distinguish which is the "quantization" of the momentum of an electromagnetic field? Of course, to learn quantum mechanics, it's actually better to know the relationship between quantum mechanics and analytical mechanics.

The rest requires classical field theory (electrodynamics) <

One of the universal theorems of dynamics. The content is that the increment of the momentum of the object is equal to the impulse of the resultant external force on which it is subjected, i.e., ft=mδv, i.e., the vector sum of the impulses of all external forces. It is defined as:

If a system is not subjected to an external force or the vector sum of the external forces is zero, then the total momentum of the system remains the same, and this conclusion is called the law of conservation of momentum. The law of conservation of momentum is one of the most important and universal conservation laws in nature, which applies to both macroscopic objects and microscopic particles; It is suitable for both low-speed moving objects and high-speed moving objects. It is a law summarized by experimental observations, and can also be deduced from Newton's second law and kinematic formulas.

This is another theory that describes classical mechanics equivalent to Newtonian mechanics, that is, Hamiltonian mechanics, in which important quantities are important.

I don't know what the subject is, I explained it according to my own understanding.

Hamiltonian mechanics is one of the manifestations of classical mechanics, which describes motion with generalized coordinates and generalized momentum, describes the evolution of coordinates and momentum with regular equations, and writes regular equations with Hamiltonian. So, to build a physical system is to build its Hamiltonian. For comparison, for Newtonian mechanics is the expression of the construction force, Lagrangian mechanics is the construction of the Rallais quantity.

For a system of particles with n particles, there are 3n coordinates in space. If there are k finite constraints between these particles, the constraint equation can be written as: fs(x1,x2,...，x3n；t)=0（s=1，2…，k）。

The constraint equation is used to eliminate k variables in 3n coordinates, leaving n=3n k variables to be independent. With variable conversion, you can use any other n independent variables q1, q2, etc, qn. Thus, 3n x coordinates can be expressed as xi=xi(q1,q2....，qn；t)（i=1，2…，3n）。

Such variables that are independent of each other are called generalized coordinates, and their number n is equal to the degrees of freedom of the complete system.

There are two commonly used generalized coordinates: linear and angular. For example, for a particle constrained to move on a fixed curve in space, the distance s measured from the starting point can be used as generalized coordinates. The particle point that swings in the vertical plane is constrained by a thin rod, and the angle between the rod and the plumb line can be used as a generalized coordinate. The derivative of generalized coordinates versus time is called generalized velocity.

Similarly, because the problem requires that there will also be generalized acceleration, generalized momentum, generalized angular momentum, etc.

The generalized momentum is integrated into the generalized coordinates in one cycle, which is equal to an integer multiple of the pure curvature of the Frank constant, and ......I don't write the slippery formula, I don't know why different books are not the same, and I don't know why ...... dust is not the same

How can helium atom double electron eggplant friends use classical mechanics, Bohr's orbital theory can only calculate hydrogen atoms, double electrons are very complicated, classical Tunatsa mechanics needs orbital radius or something, or quantum mechanics is more reliable, of course, the calculation results are also approximate, this talent is shallow, in this class to get a number of eggplant axes.

Mei Qiangzhong, "Water Wave Dynamics".

Engineering Fluid Mechanics

Publisher: Tongji University Press.

Publication date: May 1999.

Size: 16 pages.

Page: 226

Introduction. This book is written according to the basic requirements of the engineering fluid mechanics course of the building structure major in colleges and universities, focusing on the basic concepts and the application of fluid mechanics in engineering, and strives to be simple and suitable for readers to learn by themselves

The book is divided into 10 chapters, including: Introduction, Hydrostatics, Fluid Kinematics, Ideal Fluid Dynamics, Similarity Theory, Flow in Circular Tubes, Basic Theory of Vortices, Plane Potential Flow Theory, Viscous Fluid Dynamics, and Wave Theory

This book can be used as a textbook for architectural structure majors, environmental majors, marine engineering and other majors, and can also be used as a reference for relevant engineering and technical personnel

Directory. Chapter I: Introduction.

1-1 Content and methods of engineering fluid mechanics research.

1-2 A brief history of fluid mechanics.

1-3 Introduction to the System of Units.

1-4 Macroscopic model and physical properties of fluids.

Chapter 2 Hydrostatics.

2-1 Hydrostatic pressure and its characteristics.

2-2 Basic Equations of Statics and Their Applications.

2-3 The force exerted by the stationary fluid on the plate.

2-4 The force exerted by the stationary fluid on the cylindrical surface.

2-5 The force exerted by the stationary fluid on the surface - buoyancy.

2-6 Stability of buoyants and submersibles.

2-7 Relative balance.

Chapter 3 Fluid Kinematics.

3-1 Two methods for studying fluid motion.

3-2 Geometric representation of the velocity field.

3-3 Continuity equation.

3-4 Continuous equations for curvilinear coordinate systems.

3-5 Analysis of fluid micromass motion.

3-6 Concept of spin-free motion of fluids.

In fact, the formula v is using Lagrangian multiplication to solve the extremum. Lagrangian multiplication: given the binary function z= (x,y) and the additional condition (x,y)=0, in order to find the extreme point of z= (x,y) under the additional condition, first do the Lagrangian function, where is the parameter.

Find the first-order partial derivatives of l(x,y) for x and y so that they are equal to zero and are coupled with additional conditions, i.e. .

l'x(x,y)=ƒ'x(x,y)+λ'x(x,y)=0，l'y(x,y)=ƒ'y(x,y)+λ'y(x,y)=0，(x,y)=0

From the above system of equations, x,y and , and (x,y) are thus obtained, which is the possible extremum of the function z= (x,y) under the additional condition (x,y)=0. Therefore, the formula v is the constructed Lagrangian high number, if you learn the extrema of the multivariate function in the high number, it should be easy to understand, and it is generally solved by Lagrangian multiplication.

If a system is not subjected to an external force, or if the resultant external force is 0, then the momentum is conserved, and if the resultant external moment of the system is 0, then the angular momentum is conserved.

When the Lagrangian function of motion does not contain a certain generalized coordinate, then the generalized momentum of the corresponding coordinates is conserved, and when the Lagrangian function of motion does not contain time, then the generalized energy is conserved For a fixed particle, as long as the velocity changes, the kinetic energy changes For the mass system, it depends on the total kinetic energy of the system, which you had better calculate whether its kinetic energy has changed according to the conservation of energy.

For rigid bodies, kinetic energy = translational kinetic energy + rotational kinetic energy.

Momentum is directional, is a vector quantity, and refers to the tendency of this object to maintain its motion in the direction of its motion.

Kinetic energy is a type of energy that has no directionality and is the work done to bring an object from a state of rest to a state of motion.

Conservation of angular momentum: Angular momentum is a vector quantity, which refers to the directed line segment from the center of motion (instantaneous center of rotation) to the position of motion, and conservation means that the resultant external moment of the particle is 0 and the vector remains unchanged.