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Starship

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What kind of math does QM use (beyond calculus, differential equations and linear algebra)?

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- Thread starter Starship
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In summary, QM uses a variety of mathematical concepts beyond calculus, differential equations, and linear algebra. These include complex analysis, multivariate calculus, calculus of variations, Fourier analysis, functional analysis, group theory, representation theory, algebra, topology, differential geometry, probability theory, logic, symplectic geometry, and vector-cross-product math. These different branches of mathematics play a crucial role in understanding and studying quantum mechanics. Additionally, they extend beyond the basic principles of QM and are important in the fields of theoretical physics and modern analysis.

- #1

Starship

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What kind of math does QM use (beyond calculus, differential equations and linear algebra)?

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- #2

Locrian

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Some complex analysis helped me quite a bit.

- #3

Starship

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- #4

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Less on rings and fields,but a lotta group theory representations...

Daniel.

Daniel.

- #5

selfAdjoint

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Dearly Missed

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dextercioby said:Less on rings and fields,but a lotta group theory representations...

Daniel.

Unless you get beyond basic QM, when rings (in the form of algebras: rings with a product) and fields get very important. Lie algebras, Von Neumann algebras, Clifford algebras, ...

- #6

Starship

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Daniel.

P.S.Did someone mention diff.geom.for nice bundle homological & cohomological approaches to quantization (including the famous BRST)...?

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One might add Probability Theory, Logic, and Symplectic Geometry.

- #9

Starship

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- #10

NEOclassic

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Don't forget vector-cross-product math. Angular momentum and its orthogonality aspect extend not only from QM atomic orbits to also the perpenicularity of the axis of magnetic rotation of the Milky Way relative to the plane of matter. Cheers, Jim

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Quantum mechanics is a branch of physics that studies the behavior of matter and energy at a very small scale, such as atoms and subatomic particles.

Math is essential in quantum mechanics as it provides a way to describe and understand the behavior of particles at the quantum level. In quantum mechanics, math is used to calculate probabilities, describe wave functions, and make predictions about the behavior of particles.

Classical mechanics describes the behavior of macroscopic objects, while quantum mechanics describes the behavior of particles at the subatomic level. Classical mechanics follows deterministic laws, whereas quantum mechanics follows probabilistic laws. Additionally, classical mechanics is based on Newton's laws of motion, while quantum mechanics is based on the principles of wave-particle duality and uncertainty.

The uncertainty principle states that it is impossible to know both the position and momentum of a particle with absolute certainty. This principle has significant implications in quantum mechanics as it means that the behavior of particles cannot be predicted with 100% accuracy, and there will always be a level of uncertainty in our measurements.

Quantum mechanics has many practical applications, including in technology such as transistors, lasers, computer chips, and medical imaging devices. It is also used in cryptography for secure communication and in developing new materials with unique properties. Additionally, the principles of quantum mechanics are being applied in quantum computing, which has the potential to greatly improve computing power and solve complex problems that are difficult for classical computers.

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