# Why Is Task 2 in Quantum Mechanics Homework Difficult?

• Yuli10
In summary, the conversation involves a person seeking help with a physics homework problem and another person providing guidance and suggesting a method for solving the problem. The specific problem discussed is task 2, which involves determining the probability density in quantum mechanics and finding the eigenfunctions of the Hamiltonian for the infinite square well. The suggested approach is to write the wavefunction as a linear combination of the normalized eigenfunctions and calculate the probability using the coefficient associated with the eigenfunction.
Yuli10

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Hi Yuli,
Have you made any attempts or do you have any ideas of how to solve task 2? What is the general equation for determining the probability density in quantum mechanics? Please give a bit more of your thought process so we can help you out!

Cheers,
Kamas

this is what i have tried to do, some ideas of mine.

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Try starting out by finding the eigenfunctions of the Hamiltonian for the infinite square well. Each of them should be associated with a definite energy. After that, write the wavefunction as a linear combination of the normalized eigenfunctions. The probability of measuring E_n for the particle is just |c_n|^2, where c_n is the coefficient in front of the eigenfunction.

and B= square root of (12/b)

I understand that quantum mechanics is a complex and continuously evolving field of study. It deals with the fundamental nature of matter and energy at a microscopic level, and as such, it presents many challenges and problems. One of the main problems in quantum mechanics is the issue of reconciling it with classical mechanics, as the two theories have fundamentally different principles and predictions. Additionally, the concept of superposition, where a particle can exist in multiple states simultaneously, is still not fully understood and presents challenges in its application.

Regarding your specific homework problem, I can see that you have made an attempt to solve task 1, but have encountered difficulty with task 2. This is not surprising, as quantum mechanics problems often require advanced mathematical skills and a deep understanding of the underlying principles. I would suggest seeking guidance from your instructor or fellow classmates, as well as doing further research and practice to improve your understanding of the topic. Remember, it takes time and effort to fully grasp the complexities of quantum mechanics. Keep persevering and seeking help when needed, and you will eventually be able to solve even the most challenging problems in this fascinating field of science.

## 1. What is Quantum Mechanics?

Quantum Mechanics is a branch of physics that studies the behavior of matter and energy at a very small scale, such as atoms and subatomic particles. It provides a mathematical framework for understanding the behavior of particles and their interactions.

## 2. What is the problem in Quantum Mechanics?

One of the main problems in Quantum Mechanics is the measurement problem, which refers to the fact that the act of measuring a particle's properties can change its behavior. This creates a paradox between the classical and quantum worlds.

## 3. How does Quantum Mechanics differ from Classical Mechanics?

Quantum Mechanics differs from Classical Mechanics in that it describes the behavior of matter and energy at a very small scale, where classical mechanics breaks down. It also includes principles such as superposition and entanglement, which have no classical analogues.

## 4. What is the role of uncertainty in Quantum Mechanics?

The principle of uncertainty, also known as Heisenberg's uncertainty principle, states that it is impossible to know the exact position and momentum of a particle at the same time. This is a fundamental aspect of Quantum Mechanics and reflects the inherent probabilistic nature of the quantum world.

## 5. How is Quantum Mechanics used in real-world applications?

Quantum Mechanics has many real-world applications, including in the development of technologies such as transistors, lasers, and computers. It is also used in fields such as chemistry, material science, and cryptography. In the future, it is expected to play a key role in the development of quantum computing and communication technologies.

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