Shulou(Shulou.com)11/24 Report--

The original title: "ChatGPT upgrade?" Can it be admitted to the Institute of Physics when it takes the postgraduate entrance examination? "

March 15 is supposed to be an ordinary day for editors to move bricks diligently, but as soon as the editor wakes up, he finds that his moments have been scrubbed by ChatGPT:

The new version of GPT-4 is shocking!

Big upgrade! Strong enough to explode!

These words aroused my interest, so the editor quickly entered (ke) into the gpt-4. After a simple experience, the editor found that the thinking depth of Chatgpt had indeed improved by leaps and bounds than before, and his knowledge of high school and even his freshman and sophomore year could not stop it at all, so the editor was ready to test it further.

If you don't know what ChatGPT is, you can take a look at our previous tweets: some people say that ChatGPT has a PhD in physics? Our test results are impressive.

We have briefly tested the physical level of ChatGPT in the previous post, but the results are not satisfactory. It still stays in the stage of limited knowledge of physics, a lot of knowledge is limited to know, a little deeper began to look around him, logical thinking ability is limited, but that is the previous version of gpt-3.5.

Comparison of scores between gpt-4 and gpt-3.5 in various exams according to official publicity, the newly launched gpt-4 has far exceeded gpt-3.5 in all exams, has reached the human level in many majors and academics, and has even reached the top college level in the two subjects of the GRE (American Graduate entrance examination).

So the editor began to wonder: can it conquer GRE, can it conquer the postgraduate entrance examination questions of our Institute of Physics?

The postgraduate entrance examination specialized course of the Institute of Physics is an independent proposition of the National University of Science and Technology. According to the situation in previous years, only with a single subject score of about 130 (out of 150) can I be sure of being admitted.

Source: the official website of the National University of Science and Technology has different examination requirements for different majors, so here we will take the most difficult of the four mechanics as the benchmark to examine the physical level of the new version of Chatgpt. As for why quantum mechanics is chosen, because universal physics is no longer a threat to it and cannot measure its upper limit of ability, it is time for Chatgpt to see the real power!

Warm Tip: do not understand and do not affect you directly to the end of the article to read the conclusion.

01. The first question of quantum mechanics

The first question

The three questions of the first question are all basic contents of quantum mechanics, which belong to the delivery questions, but from this answer, we can see that ChatGPT has the foundation of quantum mechanics: can fully understand the topic I give, clear and correct thinking, plus ten points!

The second question

Chatgpt uses a strange method in this question. Because the topic does not give the specific form of the bound state, there is no symmetry worth discussing, so we can only give a little score.

In fact, the expected value of the mechanical quantity in the steady state does not change with time, and the specific displacement is d/dt=0, which can be derived from the Heisenberg equation of motion.

= m*d/dt=0, so the momentum expectation is 0.

The third question

In fact, this problem only needs to replace the solution of the time-dependent Schrodinger equation into the steady-state equation and find out that its derivative to time is 0, but Chatgpt takes great pains to find the solution of the time-dependent Schrodinger equation. In fact, this conclusion can be used directly.

And Chatgpt is still short: it is proved that the derivative to time is 0, but the effect is not significant.

Score on the first question: 22.

02. The second question of quantum mechanics

The first question

First of all, the eigenstate is fine, but normalization is wrong. The result of the integral should use the delta function, otherwise the whole space integral of 1 is positive infinity. But if we continue to follow the wrong thinking of Chatgpt, we will see that AI gives this result in the final step of simplification:

The value of this formula should be 1 / π. I can't believe there is such a low-level mistake, Chatgpt, you are still not trained enough!

The second question

The second question goes too far with the Taylor formula. The two conclusions in this question are Hermitian conjugate, and only one of them needs to be proved. The idea of solving the problem is to insert a complete set into the two terms, and the conclusion can be obtained by integral after operation.

The third question

At first glance, the process of the third question is reasonable, and the formula itself is correct, but AI misapplied the formula and led to the wrong result. The correct formula is as follows:

The fourth question

The fourth question Chatgpt's train of thought is right, only need to square the result of the third question to get the result, but the fourth question needs to use the conclusion of the third question, so it is also wrong, probably can give some ideas points as appropriate.

Score of the second question: 10 points.

03. Question 3 of Quantum Mechanics

First, let's take a look at Chatgpt's understanding of angular momentum.

It seems that Chatgpt does not understand angular momentum. After talking a lot of nonsense, he calculates a zero. The correct solution should replace the spherical coordinate into the wave function, and then calculate the angular quantum number 1 in the form of spherical harmonic function.

If the total angular momentum is 0 and the result of the second question is 0 directly, there is no need to calculate it.

The second question

Sure enough, after a long circle of Chatgpt nonsense, we still get 0. The first question is that the total angular momentum is miscalculated, and the second question component is bound to be miscalculated.

As for the third question, I made a mistake in the middle of AI's nonsense, so I won't take a screenshot.

The third question score: 2 points.

04. Question 4 of Quantum Mechanics

The first question

The idea of solving the first question is correct, but Chatgpt miswrote the Hamiltonian as soon as it came up, missing 1 and 2 in the Pauli matrix, so there is an extra 2 in the final eigenvalue, and the result is not normalized, but otherwise it is all right.

The second question

The second question is the pure eigenvalue calculation problem, the idea of Chatgpt is very standard, and the previous calculation is also correct, but the two 2c_0 are thrown away directly in the final calculation of the determinant, resulting in the wrong results of the two energy levels. Although it's not all right, it's great to be able to do this.

Question 4 score: 25 points

05. The fifth question of quantum mechanics

The first question

The first question is to send sub-questions. As long as the uncertainty of steady-state momentum and displacement is substituted into the uncertainty relationship, the minimum value can be derived from a ^ 2 + b ^ 2 ≥ 2ab. Although the train of thought of Chatgpt is a bit complicated, it has no problem, but it is both wrong:

But after a little calculation, we can see that the result of the simplification here should be:

The second question

Second, when asked about the variational method, Chatgpt miscalculated the normalized constant as soon as it came up:

But humans can also make such low-level mistakes.

Obviously, AI misses the square here, which leads to all errors in subsequent calculations. But the process given by AI is standard, well-organized and worth learning.

The third question

This question directly covers the properties of the rise and fall operator: await-| 0 > = 0, | 1 > = axiom + | 0 >. The ground state wave function is determined by the first formula, and then the first excited state is calculated by the second formula. AI uses the same idea, but miscalculates the derivative in the next step.

The fourth question

The topic has given the matrix form of perturbation, and the problem can be solved by directly calculating the eigenvalues, but Chatgpt miscalculated the simple determinant and worked out the amazing hand of 1: 1: 2:

The correct duration equation should be-λ ^ 3 + λ = 0, not-λ ^ 3 = 2 λ = 0. The three eigenvalues of 0 and ±1 are solved from the duration equation, so the triple degeneracy is eliminated under perturbation, and the energy level is split into three eigenvalues corresponding to one to one.

Total score of question 5: 18.

ChatGPT total score: 77 points / 150 points, there is still a gap of 100 million points from the goal of 130 points, it is recommended to fight again in the second year!

In addition, I also asked Chatgpt to do a large number of postgraduate mechanics exams in 2021, and it also got about 80 points, and if you can help it slightly correct the errors in the calculation process, it can reach about 100 points. It is no exaggeration to say that Chatgpt's quantum mechanics has reached the level of physics graduates.

06. Literature summary in order to further test the academic ability of gpt-4, I found another article to test the literature reading ability of gpt-4. The following is a summary of the literature generated by it.

Paper link

There are many errors in Chatgpt translation, such as the unit of temperature mK is translated into milligrams, and some academic terms can not be understood, such as 1K pool (4He-1K-stage) is translated into 1K class, do not know Kapicha thermal resistance, etc., the reference value is limited. It seems that the translation of academic terms is not an easy task even for AI.

However, if Chatgpt is allowed to output in English, its ability to summarize the content of the literature is very strong, the language is fluent and logical, but it will still leave out some important information, so it is not possible to rely on AI to read the literature.

At present, it is troublesome to input the paper into Chatgpt. In many cases, it is better to read the abstract directly, which can not provide substantial help for us to read the literature. If the main content can be given directly according to the picture or pdf, it will be another leap in its ability.

07. Comparison between the old and new versions finally I compared the quantum mechanical capabilities of gpt-3.5 and gpt-4. Facing the problem of one-dimensional harmonic oscillator, gpt-4 can solve it perfectly, but gpt-3.5 can not.

Test content related source: however, in the face of more complex Dirac equations and fine structure problems of hydrogen atoms in field theory, even gpt-4 can do nothing but report errors after saying a lot of nonsense. It seems that the difficulty of field theory has exceeded its upper limit. Generally speaking, gpt-3.5 has only a general understanding of quantum mechanics, but gpt-4 has a deep understanding of quantum mechanics, which is much higher than that of gpt-3.5.

Comparing gpt-3.5 with gpt-4, the first screenshot is gpt-3.5 and the last three are gpt-4. In summary, after testing, gpt-4 has a deep understanding of quantum mechanics. Its idea of solving problems is clear and accurate, but its computing ability is poor. Due to the limitations of the underlying logic of the language model, it always makes low-level calculation mistakes in the process of solving problems, so it can not get a high score, so it will not be admitted to the Institute of Physics. But I don't think it's a problem for its total score to cross the national line.

Although it is difficult for ChatGPT to be admitted to the Institute of Physics, its quantum mechanics level is close to that of physics graduates (except computing power), which makes people have to admit that it is powerful. Not only that, the problems learned from primary school to undergraduate can be solved by ChatGPT, which can not only provide detailed ideas and process, but also explain the questions you ask. Good use can be a good helper for students.

Finally, welcome to apply for the Institute of Physics of the Chinese Academy of Sciences.

Note the 1:ChatGPT web page is not open for picture input. This article asks ChatGPT questions in the form of input symbols rather than pictures. The title pictures displayed are for the convenience of readers.

Note 2: the editor has no experience in the postgraduate entrance examination, and the score is relatively random. This article does not constitute any suggestions for the postgraduate entrance examination.

This article comes from the official account of Wechat: Institute of Physics, Chinese Academy of Sciences (ID:cas-iop), author: Huang Shuiji

Welcome to subscribe "Shulou Technology Information " to get latest news, interesting things and hot topics in the IT industry, and controls the hottest and latest Internet news, technology news and IT industry trends.