Exploring Heisenberg's Matrix Mechanics: Applications & Solutions

[jack47]

I was just wondering about Heisenbergs matrix mechanics, what does it look like? is it still usefull to solve certain problems? does anyone know a decent link that explains it properly? (I've had a look but found nothing detailed enough)

I know Hilbert proved it was equivalent to Schroedinger's method, but sometimes 2 equivalent methods can be very different when applied to certain situations.

 

[robphy]

Some links:

http://www.users.csbsju.edu/~frioux/workinprogress.html
http://www.users.csbsju.edu/~frioux/matmech/matmech.htm

http://scipp.ucsc.edu/~dine/ph101/Physics_101B.html
http://scipp.ucsc.edu/~dine/ph101/bands.pdf
http://scipp.ucsc.edu/~dine/ph101/feynman1.pdf

 

[R0man]

Heisenberg's matrix mechanics is a mathematical framework for describing the behavior of quantum systems, developed by German physicist Werner Heisenberg in the 1920s. It involves representing physical quantities, such as position and momentum, as matrices and using mathematical operations on these matrices to calculate the probabilities of different outcomes in a quantum system.

The matrix mechanics approach is still very useful in solving certain quantum problems, especially when dealing with systems with discrete energy levels. It has been successfully applied to various areas of quantum physics, including atomic and molecular structure, nuclear physics, and particle physics.

If you are looking for a detailed explanation of Heisenberg's matrix mechanics, I would recommend checking out resources such as textbooks on quantum mechanics or online lectures from reputable universities. Some good starting points could be the MIT OpenCourseWare or the Quantum Mechanics section on the Stanford Encyclopedia of Philosophy website.

As you mentioned, Heisenberg's matrix mechanics and Schrödinger's wave mechanics are mathematically equivalent. However, they differ in their conceptual approaches to understanding quantum systems. While Schrödinger's approach views particles as waves, Heisenberg's approach focuses on the observable quantities and their relationships. Both methods have their advantages and are applicable in different situations. Ultimately, the choice of which method to use depends on the specific problem at hand and the preferences of the physicist.

In summary, Heisenberg's matrix mechanics is a powerful tool in understanding and solving problems in quantum mechanics. It is still relevant and widely used in modern physics, and there are many resources available to help you understand it better. I hope this helps answer your questions.