Stochastic metric space and quantum mechanics

Quantum mechanics in metric space: wave functions and their densities.

Hilbert space combines the properties of two different types of mathematical spaces: vector space and metric space. While the vector-space aspects are widely used, the metric-space aspects are much less exploited. Here we show that a suitable metric stratifies Fock space into concentric spheres on which maximum and minimum distances between states can be defined and geometrically interpreted. U...

Stochastic Processes and Quantum Mechanics

Hilbert Space Quantum Mechanics

1 Vectors (Kets) 1 1.1 Dirac notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Qubit or spin half . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Intuitive picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 General d . . . . . . . . . . . . . . . . . . ...

Space Structure and Quantum Mechanics

A new concept of the constitution of nature is considered. The constructed submicroscopic quantum mechanics is deterministic and is characterised by elementary excitations of the space net that is treated as the tesselation of balls, or superparticles. Said excitations called ”inertons” accompany any canonical particle when it moves. It is shown theoretically that the introduction of inertons o...

Momentum in stochastic quantum mechanics

Momentum is analyzed as a random variable in stochastic quantum mechanics. Arbitrary potential energy functions are considered. The oscillator is presented as an example.