# GRE related question in Quantum

• I
• Silviu
In summary, The conversation is about a problem involving the chlorine molecule and its covalent bond. The solution uses the uncertainty principle to find the approximate kinetic energy of one of the covalently bonded electrons. The person asking the question is confused about the use of uncertainty principle and how it relates to finding the actual energy. They question whether there may be an error in the solution.
Silviu
Hello! I was doing a GRE practice test and I came across this problem: The chlorine molecule consists of two chlorine atoms joined together by a covalent bond with length approximately 100 pm. What is the approximate kinetic energy of one if the covalently bonded electrons? And in their solution they use uncertainty principle: (100 pm)(delta p) = h => delta p = 2keV/c and then they plug this into E = p^2/2m. This is also what I would do during the exam, given the information provided by the problem. However, I am a bit confused about the correctness of the solution. The 100 pm is the actual length not the uncertainty in the length, so why can we use uncertainty principle like that? And even if that would be the case, how can you use the uncertainty in the momentum, to get the actual energy, using E = p^2/2m? Isn't something wrong here?

Silviu said:
why can we use uncertainty principle like that
Because the expectation values of both ##x## and ##p## are zero from symmetry

## 1. What is the GRE subject test in Quantum?

The GRE subject test in Quantum is a standardized exam used to assess a student's knowledge and understanding of quantum mechanics and related topics. It is often required for admission to graduate programs in physics or other fields related to quantum physics.

## 2. How is the GRE subject test in Quantum structured?

The GRE subject test in Quantum consists of 100 multiple-choice questions, divided into three sections: Classical Mechanics, Electromagnetism, and Quantum Mechanics. The test is 2 hours and 50 minutes long and is scored on a scale of 200-990.

## 3. What topics are covered in the GRE subject test in Quantum?

The GRE subject test in Quantum covers a wide range of topics, including wave-particle duality, quantum states and operators, quantum dynamics, atomic and molecular structure, and nuclear and particle physics. It also includes some classical physics topics, such as kinematics, Newton's laws, and electromagnetism.

## 4. How can I prepare for the GRE subject test in Quantum?

There are several ways to prepare for the GRE subject test in Quantum, including studying from textbooks and review guides, taking practice tests, and attending review courses or workshops. It is also helpful to review your notes and textbooks from undergraduate courses in quantum mechanics and other relevant subjects.

## 5. How important is the GRE subject test in Quantum for graduate school admissions?

The importance of the GRE subject test in Quantum varies depending on the graduate program and university. Some programs may require a high score on the exam for admission, while others may consider it as just one aspect of the overall application. It is best to check with the specific programs you are applying to for their requirements and expectations regarding the GRE subject test in Quantum.

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