# Learn QM in Heisenberg Formalism: Texts/Sources

• James Jackson
In summary, the conversation discussed recommendations for learning quantum mechanics in the Heisenberg formalism. One suggestion was the book "Quantum Mechanics" by L. Schiff and another was to check the bibliography of S. Weinberg's "Quantum Theory of Fields". The Heisenberg formalism refers to the original 1925 Heisenberg-Jordan-Born matrix mechanics, while the Heisenberg picture is something else. The suggestion was made to also check the book "Gallindo & Pascual" for a discussion of the three equivalent pictures in quantum mechanics.
James Jackson
Can anyone recommend any texts / online sources for learning QM in the Heisenberg formalism? I don't want some 'basics of' book - nitty gritty maths is what I'm after.

I've seen many texts on QM,but beside the VI-the chapter of L.Schiff's "Quantum Mechanics",McGraw-Hill,1947,i don't remember other source.

Daniel.

P.S.You may want to check the bibliography to the first chapter of S.Weinberg's "Quantum Theory of Fields",VOL 1,CUP,1995.

Thank you both, I'll follow those up. As a 'reference point', am I thinking what the Heisenberg Formalism is what it is - ie unitary evolution of the operators rather than the wavefunction (that, of course, being the Schrodinger formalism)?

"Heisenberg formalism" means just that:the original 1925 Heisenberg-Jordan-Born matrix mechanics.

As for the Heisenberg picture,that's something else.The 3 equivalent pictures should be in any serious QM text:Gallindo & Pascual,for example.

Daniel.

Ah, symantics of the words formalism and picture... Thanks for the book ref.

## 1. What is the Heisenberg formalism in quantum mechanics?

The Heisenberg formalism is a mathematical framework for studying quantum mechanics, developed by Werner Heisenberg in the 1920s. It is based on the idea that physical observables, such as position and momentum, are represented by matrices rather than classical variables. This allows for the description of quantum systems and their evolution over time.

## 2. What are some common texts or sources for learning about the Heisenberg formalism?

Some commonly used texts for learning about the Heisenberg formalism in quantum mechanics include "Quantum Mechanics" by David J. Griffiths, "Introduction to Quantum Mechanics" by David J. Griffiths and Darrell F. Schroeter, and "Principles of Quantum Mechanics" by R. Shankar. Online sources such as lectures and tutorials from universities also provide valuable information.

## 3. How does the Heisenberg uncertainty principle fit into the Heisenberg formalism?

The Heisenberg uncertainty principle, which states that certain pairs of physical quantities cannot be known simultaneously with arbitrary precision, is a fundamental aspect of the Heisenberg formalism. It arises from the fact that in quantum mechanics, the act of measuring a physical quantity disturbs the system, making it impossible to measure other related quantities with certainty.

## 4. What are the advantages of using the Heisenberg formalism in quantum mechanics?

One advantage of using the Heisenberg formalism is that it provides a more concise and elegant mathematical framework for studying quantum mechanics compared to other formalisms, such as the Schrödinger equation. It also allows for the description of symmetries and conservation laws in a more natural way.

## 5. Are there any limitations or drawbacks to using the Heisenberg formalism in quantum mechanics?

One limitation of the Heisenberg formalism is that it only applies to systems with a finite number of degrees of freedom. It also does not provide a direct way to calculate the wave function, which is needed to make predictions about the behavior of a quantum system. Additionally, it can be difficult to interpret physically, as it relies heavily on mathematical concepts such as operators and eigenvalues.

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