For all you Math / QM freaks out there

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In summary, the conversation is recommending a paper titled "Mathematical surprises and Dirac's formalism in quantum mechanics" by F. Gieres. The paper discusses the lack of a rigorous mathematical formalism in quantum mechanics and how it leads to interesting contradictions. The author provides solutions to these problems and the paper is considered mandatory reading for anyone studying QM. The paper can be accessed with a subscription or for free on arXiv in English or French.
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Edgardo
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For all you Math / QM freaks out there...

...check out this paper:
F. Gieres, Rep. Prog. Phys. 63 (2000), pp. 1893 - 1931,
"Mathematical surprises and Dirac's formalism in quantum mechanics"
which you can find here:
http://www.iop.org/EJ/abstract/0034-4885/63/12/201 (requires subscription)

You can download the paper for FREE here:
http://arxiv.org/abs/quant-ph/9907069 (English) or
http://arxiv.org/abs/quant-ph/9907070 (French).

The author shows that the lack of a rigorous mathematical formalism in QM leads to contradictions that are quite interesting. He illustrates problems and also gives solutions to them how to avoid them.

Have fun!
 
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FAQ: For all you Math / QM freaks out there

What is QM?

QM stands for quantum mechanics, which is a branch of physics that studies the behavior of particles at a subatomic level.

Why is QM important?

QM is important because it helps us understand the fundamental principles and laws that govern the behavior of matter and energy at a microscopic level. It has also led to many technological advancements, such as transistors and lasers.

What is the difference between classical mechanics and quantum mechanics?

Classical mechanics describes the behavior of macroscopic objects while QM describes the behavior of microscopic particles. Classical mechanics follows deterministic laws, while QM introduces uncertainty and probability into the equations.

How does QM relate to math?

QM heavily relies on mathematical concepts and equations to describe and predict the behavior of particles. The mathematics used in QM includes linear algebra, calculus, and probability theory.

Is QM difficult to understand?

QM can be challenging to understand because it goes against our everyday experiences and intuition. However, with dedication and practice, anyone can gain a basic understanding of its principles and applications.

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