Search results
Results from the WOW.Com Content Network
Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics.
Heisenberg's matrix mechanics formulation was based on algebras of infinite matrices, a very radical formulation in light of the mathematics of classical physics, although he started from the index-terminology of the experimentalists of that time, not even aware that his "index-schemes" were matrices, as Born soon pointed out to him.
In vector logic, the matrix-vector structure of logical operators is an exact translation to the format of linear algebra of these Boolean polynomials, where the x and 1−x correspond to vectors s and n respectively (the same for y and 1−y). In the example of NAND, f(1,1)=n and f(1,0)=f(0,1)=f(0,0)=s and the matrix version becomes:
The most notable difference between quantum logic and classical logic is the failure of the propositional distributive law: [1]. p and (q or r) = (p and q) or (p and r),. where the symbols p, q and r are propositional variables.
For functions in certain classes, the problem of determining: whether two functions are equal, known as the zero-equivalence problem (see Richardson's theorem); [5] the zeroes of a function; whether the indefinite integral of a function is also in the class. [6] Of course, some subclasses of these problems are decidable.
The definition of quantum theorists' terms, such as wave function and matrix mechanics, progressed through many stages.For instance, Erwin Schrödinger originally viewed the electron's wave function as its charge density smeared across space, but Max Born reinterpreted the absolute square value of the wave function as the electron's probability density distributed across space; [3]: 24–33 ...
The BFSS matrix model can therefore be used as a prototype for a correct formulation of M-theory and a tool for investigating the properties of M-theory in a relatively simple setting. The BFSS matrix model is also considered the worldvolume theory of a large number of D0- branes in Type IIA string theory.
A permutation matrix is a (0, 1)-matrix, all of whose columns and rows each have exactly one nonzero element.. A Costas array is a special case of a permutation matrix.; An incidence matrix in combinatorics and finite geometry has ones to indicate incidence between points (or vertices) and lines of a geometry, blocks of a block design, or edges of a graph.