How important is experience in QM?

[reilly]

How important is practical experience with quantum mechanics for understanding, as best as one can, the subject?

For example: Weinberg in his QFT tome, briefly discusses QFT three point interactions in terms of angular momentum states. So, he points out that the interaction can be formulated with 3-j symbols. How would you do Born approx. for pion-nucleon scattering in the angular momentum rep .

Or compute the numerical value(s) for the 1p-1s transition for the hydrogen atom, with the Coulomb gauge and non-rel QED.

Does a separable potential in non-rel many-body theory imply and energy gap?

Just curious.
Regards,
Reilly Atkinson

 

[azntoon]

Practical experience with quantum mechanics is very important for understanding the subject. Not only does it provide a hands-on approach to the material, but it also allows one to gain a deeper understanding of the underlying concepts. This is especially true when dealing with more complex topics like scattering theory and many-body systems. By working through these problems, students can gain a better appreciation for the nuances of the mathematical models used to describe quantum systems. Additionally, it can help them to better appreciate how different physical scenarios can lead to vastly different results.

 

[denian]

Experience is extremely important in quantum mechanics (QM). It is not enough to simply understand the mathematical equations and principles of QM, practical experience is necessary to truly grasp the subject. This is because QM deals with the microscopic world where classical intuition and common sense do not apply. Only through hands-on experience can one truly appreciate the counterintuitive nature of QM and develop an intuitive understanding of its concepts.

In the example given, Weinberg's use of 3-j symbols to describe three point interactions in QFT may seem abstract and disconnected from practical applications. However, a person with practical experience in QM would understand the significance of using angular momentum states in this context. They would also understand how to apply this knowledge to solve problems, such as the Born approximation for pion-nucleon scattering.

Similarly, in the case of computing numerical values for the 1p-1s transition in the hydrogen atom, practical experience with QM is crucial. This involves not only understanding the equations and principles of QM, but also having the skills to apply them in the Coulomb gauge and non-relativistic QED. Without this practical experience, one may struggle to accurately compute the transition values.

In non-relativistic many-body theory, the concept of a separable potential is often used to simplify calculations. However, only through practical experience can one understand the implications of a separable potential and whether or not it implies an energy gap. This is because practical experience allows one to see how the concept applies in real-world scenarios and how it affects the results of calculations.

In conclusion, while theoretical knowledge is important in QM, practical experience is equally crucial for a thorough understanding of the subject. It allows one to bridge the gap between theory and application, and develop an intuitive understanding of the complex concepts of QM. Without practical experience, one may struggle to fully comprehend the intricacies and nuances of this fascinating field of science.