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James Jackson
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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.
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.
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.
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.
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.
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.