mvillagra said:The math part seems really interesting too, it is mainly based on linear operators on hilbert spaces. But, it seems to me that it only uses inner product (pre-hilbert) spaces, then why these authors (and also paper authors) refers always to hilbert spaces?
mvillagra said:thank you very much for your answers, that was fast!
I will certaintly take a look at these tips!
Quantum mechanics is a branch of physics that studies the behavior and interactions of subatomic particles, such as electrons and photons. It provides a mathematical framework for understanding the fundamental principles of nature at a microscopic level.
Quantum mechanics is important because it helps us understand and predict the behavior of particles at the smallest scales, which has led to groundbreaking technologies such as transistors and lasers. It also plays a crucial role in fields such as chemistry, materials science, and quantum computing.
Some key concepts in quantum mechanics include wave-particle duality, superposition, and entanglement. Wave-particle duality refers to the fact that particles can exhibit both wave-like and particle-like behavior. Superposition is the idea that a particle can exist in multiple states at the same time. Entanglement is a phenomenon where two particles become connected in such a way that the state of one particle affects the state of the other, even if they are separated by large distances.
Yes, there are several introductory books on quantum mechanics written for non-scientists. These books often use analogies and everyday examples to explain complex concepts in a more accessible way. Some popular titles include "The Elegant Universe" by Brian Greene and "Quantum: A Guide for the Perplexed" by Jim Al-Khalili.
A solid understanding of calculus and linear algebra is necessary to fully grasp the mathematical concepts in quantum mechanics. It is also helpful to have some basic knowledge of classical mechanics and electromagnetism. However, many introductory books on quantum mechanics provide a review of the necessary mathematical concepts within the text.