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Learn the Basics of Hilbert Spaces and Their Relatives: Definitions Hilbert spaces are at first real or complex vector spaces, or are Hilbert spaces So all the theorems and definitions of linear algebra apply to the finite-dimensional ones and many to the infinite-dimensional ones, and we start at known ground
Why are Hilbert spaces used in quantum mechanics? In classical mechanics we use a 6n-dimensional phase space, itself a vector space, to describe the state of a given system at anyone point in time, with the evolution of the state of a system being described in terms of a trajectory through the corresponding phase space However, in quantum
Derivation of the Einstein-Hilbert Action - Physics Forums Derivation of the Einstein-Hilbert Action Abstract Most people justify the form of the E-H action by saying that it is the simplest scalar possible But simplicity, one can argue, is a somewhat subjective and ill-defined criterion Also, simplicity does not shed light on the axiomatic structure of general relativity
Hilbert spaces and quantum operators being infinite dimensional . . . The discussion centers on the realization that quantum operators X and P are not simple infinite-dimensional matrix generalizations, leading to the understanding that the space of quantum states is a "rigged" Hilbert space rather than a standard Hilbert space The original poster expresses confusion over manipulating these operators and seeks recommendations for rigorous yet practical
Banach Space that is NOT Hilbert • Physics Forums I know that all Hilbert spaces are Banach spaces, and that the converse is not true, but I've been unable to come up with a (hopefully simple!) example of a Banach space that is not also a Hilbert space Any help would be appreciated!
Why is Hilbert not the last universalist? • Physics Forums It is often said that Poincare was the last universalist, i e the last mathematician who understood more-or-less all mathematics of his time But Hilbert's knowledge of math was also quite universal, and he came slightly after Poincare So why was Hilbert not the last universalist? What branch
Difference between hilbert space,vector space and manifold? Difference between hilbert space,vector space and manifold?? Physically what do they mean? I m really confused imagining them Explanation with example would help me to understand there application THanks in advance