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A Universe from Nothing: Why There Is Something Rather than Nothing is a non-fiction book by the physicist Lawrence M. Krauss, initially published on January 10, 2012, by Free Press. It discusses modern cosmogony and its implications for the debate about the existence of God .
Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot.
One particle: N particles: One dimension ^ = ^ + = + ^ = = ^ + (,,) = = + (,,) where the position of particle n is x n. = + = = +. (,) = /.There is a further restriction — the solution must not grow at infinity, so that it has either a finite L 2-norm (if it is a bound state) or a slowly diverging norm (if it is part of a continuum): [1] ‖ ‖ = | |.
Quantum mechanics is the study of matter and its interactions with energy on the scale of atomic and subatomic particles.By contrast, classical physics explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the moon.
In the late 1920s, the then new quantum mechanics showed that the chemical bonds between atoms were examples of (quantum) electrical forces, justifying Dirac's boast that "the underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known". [24]
A common example of quantum numbers is the possible state of an electron in a central potential: (,,,), which corresponds to the eigenstate of observables (in terms of ), (magnitude of angular momentum), (angular momentum in -direction), and .
All attempts to grapple with atomic phenomena using classical physics were eventually frustrated, he wrote, leading to the recognition that those phenomena have "complementary aspects". But classical physics can be generalized to address this, and with "astounding simplicity", by describing physical quantities using non-commutative algebra. [13]
In mathematical physics, geometric quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory. It attempts to carry out quantization, for which there is in general no exact recipe, in such a way that certain analogies between the classical theory and the quantum theory remain manifest.
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