basic inclusions of spheres 6 in number inside a rectangular format….

———————————-displacement = S/16———————————>

height = 16 S as basic formulation for Area….

basic definition of a half circkle as the circumference of 6  representations =2 pi r /6

as 1/2 . 2 pi r . 6

total circumference = 6 pi r

area as volume of circle = 12 pi r

area / cir = vol

relation = S / 16 = 16 S / A

as linear 1 -D

= S / 16 . A = 16 S

linear 2 -D connection

by S. A = 1

2 = alternations of 2S reflection by

S= A

to use the basis of a dimensional representations of the following

1) circumference of (half circle) 1/2

as area ——————> volume of 2 pi r squared in a 3 dimensional relations with;

2) a linear (half circumference ) 1/2 as Area ————–>Vol

- 1/4 2 pi r  ( as subtracted format for altering the point in a linear definition)

as area of a 2 dimensional construct…what is to be noted here is the definition

of a 2 D half circumference as 3 -D

and the 1 -D linear  format as a 2-D

as displaceing behind quant space

 

In ordinary quantum mechanics, the time-dependent one-dimensional Schrödinger equation describing the time evolution of the quantum state of a single non-relativistic particle is

\left[ \frac{-{\hbar}^2}{2m}\frac{{\partial}^2}{\partial x^2} + V(\mathbf{x}) \right] |\psi(t)\rang = i \hbar \frac{\partial}{\partial t} |\psi(t)\rang,

where m is the particle’s mass, V is the applied potential, and |\psi\rang denotes the quantum state (we are using bra-ket notation).

We wish to consider how this problem generalizes to N particles. There are two motivations for studying the many-particle problem. The first is a straightforward need in condensed matter physics, where typically the number of particles is on the order of Avogadro’s number (6.0221415 x 1023). The second motivation for the many-particle problem arises from particle physics and the desire to incorporate the effects of special relativity. If one attempts to include the relativistic rest energy into the above equation, the result is either the Klein-Gordon equation or the Dirac equation. However, these equations have many unsatisfactory qualities; for instance, they possess energy eigenvalues which extend to –∞, so that there seems to be no easy definition of a ground state. It turns out that such inconsistencies arise from neglecting the possibility of dynamically creating or destroying particles, which is a crucial aspect of relativity. Einstein’s famous mass-energy relation predicts that sufficiently massive particles can decay into several lighter particles, and sufficiently energetic particles can combine to form massive particles. For example, an electron and a positron can annihilate each other to create photons. Thus, a consistent relativistic quantum theory must be formulated as a many-particle theory.

Furthermore, we will assume that the N particles are indistinguishable. As described in the article on identical particles, this implies that the state of the entire system must be either symmetric (bosons) or antisymmetric (fermions) when the coordinates of its constituent particles are exchanged. These multi-particle states are rather complicated to write. For example, the general quantum state of a system of N bosons is written as

|\phi_1 \cdots \phi_N \rang = \sqrt{\frac{\prod_j N_j!}{N!}} \sum_{p\in S_N} |\phi_{p(1)}\rang \cdots |\phi_{p(N)} \rang,

where |\phi_i\rang are the single-particle states, Nj is the number of particles occupying state j, and the sum is taken over all possible permutations p acting on N elements. In general, this is a sum of N! (N factorial) distinct terms, which quickly becomes unmanageable as N increases. The way to simplify this problem is to turn it into a quantum field theory.

 

 

defining a law reduction in the depletion of astronomical resources as the definitions of

unalterable values on a process defined as quantal NOW responses by 3 x occilations

of the ;

1) reduction

2) depletion

3)unalterability

as the positionality taken on any parameter in space time as

the certainty of processing NON x involvements by their

recognitive similarity to processess of the involvance by 1/B

occilations in the frequencies of a connective sequence of astronomical bodies..

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