Matrix Mechanics for the Bored Wave Mechanics Student

In summary, there are major differences between wave mechanics and matrix mechanics, with the latter being a more general and abstract formalism. For someone interested in studying it, books such as J. Townsend's text and J.J. Sakurai's text are recommended, with Dirac's Quantum Mechanics also being a valuable resource. It should be noted that most sources on quantum mechanics primarily cover wave mechanics, with matrix mechanics often being mentioned briefly in relation to topics such as angular momentum.
  • #1
wavemaster
18
0
For someone who's bored with wave mechanics, would you suggest studying Heisenberg's matrix mechanics (which was the first formulation)?

Are there any major/conceptual differences? (except one talks about waves and the other doesn't!)
And for someone who wants to study it, what books/online docs would you suggest? Damn, all QM I have ever found covers wave-mechanics majorly, and some briefly mention matrix mechanics when the title hits angular momentum.
 
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  • #2
Look at J. Townsend's text; if you find it too pedantic try J.J. Sakurai. Both are certainly in your school's library.

A short answer - there are major superficial differences. The "matrix mechanics" as you call it is a very general and abstract formalism; wave mechanics falls out easily as a special case. It is often more useful to work with waves, where everything is in differential equations.
 
  • #3
Read Dirac's Quantum Mechanics.
regards,
Reilly Atkinson
 

FAQ: Matrix Mechanics for the Bored Wave Mechanics Student

1. What is Matrix Mechanics?

Matrix Mechanics is a mathematical formalism in quantum mechanics that describes the behavior of particles in terms of matrices and their operations. It was developed by Werner Heisenberg and Max Born in the 1920s as an alternative to the wave mechanics approach.

2. How does Matrix Mechanics differ from Wave Mechanics?

Matrix Mechanics and Wave Mechanics are two different mathematical approaches to understanding quantum mechanics. While Wave Mechanics describes the behavior of particles using wave equations, Matrix Mechanics uses matrices and their operations to describe particle behavior. They are both equally valid and can be used to solve different types of problems in quantum mechanics.

3. Why was Matrix Mechanics developed?

Matrix Mechanics was developed in response to the limitations of the wave mechanics approach. At the time, wave mechanics was unable to explain certain phenomena, such as the discrete energy levels of atomic systems. Matrix Mechanics provided a more general and mathematically elegant approach to understanding quantum mechanics.

4. How is Matrix Mechanics used in practical applications?

Matrix Mechanics is used in various fields of physics, including atomic and molecular physics, solid state physics, and nuclear physics. It is also used in engineering and technology, such as in the development of quantum computers and other quantum technologies.

5. Is Matrix Mechanics difficult to understand?

Matrix Mechanics can be challenging to grasp at first, as it involves complex mathematical concepts and requires a solid understanding of linear algebra. However, with practice and patience, it can be understood and applied effectively. There are also many resources available, such as textbooks and online tutorials, to help students learn Matrix Mechanics.

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