At what moment did you feel like you didn t learn quantum mechanics in vain?

In quantum mechanics, the state of a physical system is represented by a state function, and an arbitrary linear superposition of the state function 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. (In general, quantum mechanics does not definitively predict a single outcome for an observation.)

Instead, it predicts a set of different outcomes that may occur and tells us the probability of each outcome occurring. That is, if we measure a large number of similar systems in the same way, each of which starts in the same way, we will find that the result of the measurement is a certain number of occurrences, a different number of times for b, and so on. One can predict an approximation of the number of occurrences of a or b outcome, but cannot make predictions about a specific outcome for individual measurements.

The modulus 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 notation, the state function, denoted by <|AND |> denotes that the probability density of the state function is denoted by =< |denotes that its probabilistic flow density is expressed in (?2mi) ( indicates that its probability is the spatial integral of the probability density.

A state function can be expressed as a state vector in an orthogonal set of spaces, such as , where |i> is the orthogonal space base vector to each other, and is the Dirac function, satisfying the orthogonal normalization property. The state function satisfies the Schrödinger wave equation, and the evolution equation in the non-explicit state can be obtained by separating the variables, where en is the eigenvalue of the energy and h is the Hamiltonian operator. <>

If, for example, the mathematical model of quantum mechanics describes the complete physical phenomena within its scope of application, we find that the significance of the probability of each measurement in the measurement process is different from the probability in classical statistical theory. Even measurements from the exact same system will be random. This is not the same as the probability results in classical statistical mechanics.

In classical statistical mechanics, the difference in measurement results is due to the inability of the experimenter to replicate a system exactly, not because the measuring instrument cannot accurately perform the measurement. In the standard interpretation of quantum mechanics, the randomness of measurement is fundamental, and it is derived from the theoretical foundations of quantum mechanics. Since quantum mechanics, although unable to predict the outcome of a single experiment, is still a complete description of nature, one has to draw the following conclusions:

There is no objective system characteristic that can be obtained from a single measurement. The objective properties of a quantum mechanical state can only be obtained by describing the statistical distribution embodied in the whole set of experiments. Albert Einstein ("Quantum mechanics is incomplete", "God doesn't roll dice") and Niels Bohr were the first to argue about this issue.

Bohr maintains the principle of uncertainty and complementarity. Over the course of years of heated discussions, Einstein had to accept the uncertainty principle, while Bohr weakened his complementarity principle, which eventually led to today's Copenhagen interpretation.

Today, most physicists accept the idea that quantum mechanics describes the knowable properties of all systems, and that the measurement process cannot be improved because of our technical problems. One consequence of this explanation is that the measurement process perturbates the Schrödinger equation, causing the system to collapse to its eigenstate. In addition to the Copenhagen interpretation, a number of other interpretations have been proposed.

Quantum mechanics is a branch of physics that studies the motion laws of microscopic particles in the material world, mainly studying the basic theory of the structure and properties of atoms, molecules, condensed matter, atomic nuclei and elementary particles, which together with the theory of relativity constitute the theoretical basis of modern physics. Quantum mechanics is not only one of the basic theories of modern physics, but also widely used in disciplines such as chemistry and many modern technologies.

At the end of the 19th century, it was discovered that the old classical theories could not explain microscopic systems, so through the efforts of physicists, quantum mechanics was created in the early 20th century to explain these phenomena. Quantum mechanics has fundamentally changed our understanding of the structure of matter and its interactions. With the exception of gravity, which is described by general relativity, all fundamental interactions to date can be described within the framework of quantum mechanics (quantum field theory).

Maybe Einstein's time did not find a formula to unify the four physical forces, and there is a certain reason for the level of mathematics at that time, maybe the whole mathematics and the whole mathematical formula, z=syw is a miracle that happened in China in the Internet era, the overall mathematical formula is different from any mathematical formula in the past is that the overall mathematical formula is also the law of global cosmology, the universe may come from the vacuum quantum fluctuations, the so-called observable universe outside is the vacuum, the vacuum and the observable universe are one, can inspire people's understanding of the universe lifeFor example, according to the laws of integral cosmology, it is discovered that the fifth force is the dynamic equilibrium force of the universe as a whole!

Quantum mechanics is a method of calculation in the microscopic world, and the result is the rejection rate. It's too complicated and unnecessary.

When writing science fiction, a lot of creative inspiration comes from quantum mechanics.

Got it. Quantum physics is a branch of physics that studies the laws of motion of microscopic particles, and the theory of quantum physics holds that the direction of motion of particles is uncertain, and the atoms of objects are entangled.

I don't understand, because I've never heard of anything like this, and the things I'm exposed to around me are not so profound.

Quantum mechanics is a scientific theory that studies the microscopic world. Let's put it this way, everything in the world is made up of elementary particles such as atoms and electrons. You may often hear about electrons, atoms, protons, neutrons, and so on.

Those particles are the most basic particles that make up our macrocosm. You may hear the word "quantum" almost always associated with quantum mechanics, quantum communication, or quantum entanglement. But what exactly is "quantum"?

Is it smaller than an electron, an atom?

Quantum mechanics (quantum mechanics), it is a sub-discipline of physics that studies the motion laws of microscopic particles, it mainly studies the basic theory of the structure and properties of atoms, molecules, condensed matter, as well as atomic nuclei and elementary particles, and it forms the theoretical basis of modern physics together with the theory of relativity.

Quantum mechanics tells us:1The law of the world is that there is no law, and its essence is that everything is possible under the rule of probability, whether it is the law of cause and effect, the law of fiction and reality.

2.We come from nothingness to nothingness. 3.

The world has n dimensions of space, and we are only imprisoned in one of them. 4.Time does not exist, and our sense of time is nothing more than a memory or trace left by the infinite cutting of the space in which all moving matter is.

5.The world we see and think is not the world we see and think, and the reason why we regard the world we see as the world we think is an illusion given by our consciousness in order to make us adapt (the reason is that we are always using and have to perceive everything with the perceptual experience of the dimensional space in which we live).

Scientists are exploring the universe for the progress of mankind, and in the Internet era, everyone can use practice to test, if it is right, it can be adhered to, and if it is wrong, it can be corrected. Maybe Einstein's time did not find a formula to unify the four physical forces, and there is a certain reason for the level of mathematics at that time, maybe the whole mathematics and the whole mathematical formula, z=syw is a miracle that happened in China in the Internet era, the overall mathematical formula is different from any mathematical formula in the past is that the overall mathematical formula is also the law of global cosmology, the universe may come from the vacuum quantum fluctuations, the so-called observable universe outside is the vacuum, the vacuum and the observable universe are one, can inspire people's understanding of the universe lifeFor example, according to the laws of integral cosmology, it is discovered that the fifth force is the dynamic equilibrium force of the universe as a whole!

For example, according to scientific experiments about vacuum, vacuum is not nothing, but will randomly produce positive and negative virtual particles, when the positive and negative virtual particles collide and then converted into the energy of the vacuum, the vacuum is unstable, the vacuum quantum ups and downs, is the energy, mass, space-time **!

To this day, quantum mechanics is only a toy for a very small number of people, and it has nothing to do with the vast majority of people who study classical physics. Moreover, quantum mechanics claims that people who study classical physics cannot touch quantum mechanics, because those who study quantum mechanics must believe in the doctrine of quantum mechanics. And the premise of believing is that there is no preconceived classical mechanics!

Extending quantum mechanics, strange theories emerge one after another. So ghosts and gods also existed, so the ancients were still alive, so eating a health supplement and drinking pure water were quantum, as if quantum was omnipotent. Actually, stripped of the cloak of science, a farce it is still a farce!

Chinese Chinese.

Yu Xia came to China, and the sages of Heluo took the gossip.

Nine chapters of arithmetic Pythagorean strings, the law of the garden and the law of the circle push the quantum flower.

Zeng Jin's words are too terrifying, too brief.

It's better to look at Grandpa Ke's.

In fact, it is not important to do the questions, the important thing is to understand physics through examples. The first time I took a quantum mechanics class, I handed in a **, and after reading it, the teacher gave me a piece of paper with 100 quantum mechanics questions written on it, and he said that if he did all these questions, he would not have to use it in class. I really went back and did all the feasts, and the answers were written in a notebook, and each question could be studied as a small topic.

You learn in a scientific way, you can really learn a lot, and you don't find it boring. Of course, I had been playing Mathematica for three years at the time, and the computer was responsible for any math problems, and I was only responsible for understanding physics, so the tools were important. In these years, don't solve differential equations by yourself, and spend all your energy on mathematics, so how can you appreciate the beauty of physics?

I have always been very struggling with mathematics, and I feel that I may not be able to study physics.

Looking at the leader's speech, every time I feel that the admiration is like tearing down the surging river, the gap between people and people is so big...

Generally speaking, it is similar to that of a maple.

Mathematica's symbolic arithmetic and parsing capabilities are much more powerful than Maple's, and it's C-based, which is more convenient.

However, in terms of auxiliary physics, it is still Mathematica + MATLAB, the latter has great advantages in numerical operations, reading books, and understanding ideas.

This discussion thread about quantum mechanics,To my surprise, there are no words related to philosophy,Is quantum mechanics mathematics or philosophy? It's not that no one can really ...

1.In my junior year, a girl from the Department of Chemistry came to me and asked me about my physical chemistry assignment, comparing the data answered by the experiment with the data calculated theoretically, in fact, the so-called theoretical calculation data is to use the existing data to solve the Schrödinger equation of a one-dimensional infinitely deep potential well, and then I helped her solve the equation. The theoretical data and the experimental data are not often consistent with Li Hui, and while pretending to be successful, he also feels the magic of Chunhu to the application of physics in chemistry.

2.After graduating from university, I didn't do well in the TOEFL test, and I took a job of translating popular science books in the second half of the gap in order to be less idle. Originally, I recommended myself to translate astronomy books with Mao Sui, but later read my resume and gave me a popular science ...... on quantum mechanics & semiconductor devicesNow gnawing and gnawing in translation.

3.It's still a junior, and I'm in the basic class of acoustics. The teacher is a domestic acoustic celebrity, and he will also take on some work such as instrument design, speaker and acoustic device design outside the school.

He said that once a company approached him and asked him what accuracy he wanted to achieve in designing an instrument (I don't remember if it was a musical instrument or not, but it was an acoustic-related device), and he saw that the parameter was not right, because the uncertainty principle had been violated. No matter how high the company's price was, he didn't take the job, and he must have felt that quantum mechanics was not in vain. Actually, I was quite interested in the example he was talking about, but I didn't ask about it at the time.

What part of the acoustic device involves quantum mechanics? Graduate school studied astrophysics and did numerical simulations. In fact, advanced quantum mechanics and quantum field theory don't seem to be needed much, and these courses are not offered this semester.

But I always feel that I have a big blank in physics that I haven't touched yet, and my heart is not steady.

In the world of quantum mechanics, there is a mysterious force that can make two electrons separated by a world make some kind of connection, this force is called quantum entanglement. Using this power, I invented the quantum sister method.

Everyone has played the game of guessing boxing, and in the classic guessing game, the punches of both sides of the game are random, and the victory or defeat is also random. In the quantum guessing game, although the punches are still random, the victory or defeat is not random. For example, if you and your girlfriend guess boxing, the game will transition from the classical state to the quantum state, and due to the existence of entanglement, you will find that no matter how many games you play, you will always lose.

If one day you start winning, you're decorating...The world sums up this phenomenon in one sentence:

Do you want to win or love?