The occupied volume of the elementary particle is the measurement of the volume of the region of universe occupied by it.

The occupied volume of the quantum system is the total occupied volume of its elementary constituent particles.

If we have a quantum system consist of N interference pattern then the occupied volume of the quantum systems is always given as following linear combination.

where

and

is the set of all bosons in universe with distinct occupied volumes and is the occupied volume of the boson.

is the set all fermions in universe with distinct occupied volumes and is the occupied volume of the fermion,

is the number of the bosons identical to belonging to the i^th interfered wave of the quantum system.

is the number of the fermions identical to belonging to the i^th interfered wave of the quantum system. This number must fulfill the Pauli’s exclusion principle [1] .

Up to now the shape of all elementary particles does not approved; so suppose that in general form the occupied volume of elementary particle is representing function of its wavelength given as following:

and

For example if the shape of boson is spherical then when is completely left some spherical region of universe it will occupy another spherical region neighboring the last left region as illustrated in the following figure:

So the wavelength of the boson which is donated by is equal to twice the radius of spherical boson and hence the occupied volume of boson in this case is:

By the same way if the shape of fermion f_k is sphere then the occupied volume of fermion f_k in this case is:

Also the inverse of and is:

From the De-Broglie’s wave-particle duality the momentum of the elementary particle p is related to its wavelength by the formula: [2] where h is the Plank’s Constant, also from the theory of special relativity: [3] where v is the speed of elementary particle and c is the speed of light in vacuum and is the rest mass of elementary particle.

And hence by combination of De-Broglie’s formula and special relativity formula we find:

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However so from the Equation (1.7):

And hence and the speed of boson and the speed of fermion are:

where is the rest mass of boson and is the rest mass of fermion

, and, , , and the speed of the boson and speed of fermion are always bounded by the following equations:

Those two equations imply that the exchange of elementary particles between the quantum systems is bounded by speed of light c, and hence there is no action at distance on any quantum system in universe.

and the energy of boson and the energy of fermion are:

From the theory of special relativity the mass of the elementary matter particle m is representing function of its wavelength and its proper mass according to the following equations:

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From the theory of special relativity the relativistic total energy E of the elementary matter particle is represent- ing function of its wavelength and its proper mass according to the following equations:

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In the quantum mechanics the classical Newtonian equation of motion is replaced by another called Schrodinger’s equation. However the solution of Schrödinger equation is a wave function which is complex function of spatial and temporal coordinates with complex amplitude equal to probability of finding elementary particle at specified spatial and temporal coordinates, although the spatial coordinates is related to point-like idealization of elementary particle the temporal coordinate is not, so in region-like idealization of this waves we need to replace all spatial parameters of the wave function by occupied volumes of elementary constituent particles, so if we have quantum system consist of N interfered wave then the region-like quantum state of this quantum system at each instance of time t is representing the following ket vector:

where such that h is the plank’s constant and E is the total relativistic energy of the quantum system which is given as following:

1) The i^th component of is representing the i^th interfered wave of the quantum system with complex amplitude equal correspond to probability of finding some elementary particles absorbed by the quantum system inside the region of universe occupied by the i^th interfered wave.

2) The time derivation of is governing by partial differential equation equivalent to time-dependent Schrödinger’s equation given as following:

3) is always normalized because:

The process of creating of the quantum system is the process in which the quantum system undergoes increasing in its occupied volume due to the absorption of elementary particles from outside its occupied region.

The process of annihilating of the quantum system is the process in which the quantum system undergoes decreasing in its occupied volume due to the emission of elementary particles outside its occupied region.

The process of animating of the quantum system is the process in which the quantum system mutually fills and leaves region of universe.

The occupied path of the quantum system is the 3-dimentional path followed by it during its creating, annihilating and animating process and consists of all regions of universe occupied by its elementary constituent particles.

The creating and annihilating interaction between the quantum systems is the creating and annihilating process of two or more quantum systems in which the total occupied volume of one quantum system changed due to transformation of elementary particles from or to another quantum system.

Now we could define the unified creating and animating law that govern the behavior of quantum system during its creating, annihilating and animating processes as following:

The transformation of the occupied volume of the quantum system form initial value to final value s during the creating, annihilating interaction with other quantum systems is always governed by the following equation:

where:

The total occupied volumes of bosons and fermions absorbed by the quantum system from outside its occupied region during the time interval.

The total occupied volumes of bosons and fermions emitted from the quantum system outside its occupied region during the time interval.

The total volume of region of universe occupied by the quantum system during the time interval.

The total volume of universe left by the quantum system during the time interval.

And hence the transformation of the region-like quantum state of the quantum system consist of N interfered waves in time interval from the initial sate:

to the final state:

is always governing by the following equations:

where

, , , ,

, , and

Such that and

1) The total number of boson identical to absorbed by the i^th interfered wave during the time interval.

2) The total number of boson identical to absorbed by the i^th interfered wave during the time interval.

3) The total number of boson identical to emitted from the i^th interfered wave during the time interval.

The total number of boson identical to emitted from the i^th interfered wave during the time interval.

The total volume of region of universe occupied by all bosons identical to in the i^th interfered wave during the time interval.

The total volume of region of universe occupied by all fermions identical to in the i^th interfered wave during the time interval.

The total volume of region of universe occupied and left by all bosons identical to in the i^th interfered wave during the time interval.

The total volume of region of universe occupied and left by all fermions identical to in the i^th interfered wave during the time interval.

1) The Equation (1.19) implied the equivalent between the deference i − d―where i is a dynamical variable of the process of creating and d is the dynamical variable of the process of annihilating―and the deference o ? l― where o and l are the dynamical variables of process of animating―so this equation implied the equivalent between the dynamical variables of creating, annihilating and animating processes.

2) Although the dynamical variables of the creating and annihilating process i, d could counted by the particle counters installed outside the region occupied by the elementary constituent particles of the quantum system, the animating dynamical variables immeasurable by this way, however the Equation (1.20) implied the complete equivalents between the dynamical variable of creating, annihilating and animating process and hence for each measurable dynamical variables of the process of creating and annihilating there exist an equivalent dynamical variables of animating satisfy the Equations (1.20) and (1.21).

and the outer product (tensor product) of u and v is the m × n matrix [4] :

1) The outer product from hereinafter donated by.

2)

If and, then

.

Prove:

From the Theorem 2.1:

and

And hence from the Equation (1.21) the time evolution of the region-like quantum state of the system is given by the following equations:

1) is representing the creation-annihilation time evolution operator and is representing the animation time evolution operator.

2) We could calculate the components of using particles counters installed outside the occupied re- gion of the quantum system, however the measurement components of is very difficult but the Equation

(2.5) tell us the equivalents between the components of and.

3) the complex amplitude of the component of and in the i^th row and j^th column could interpreted as probability amplitude of transition of some elementary particle in the i^th interfered wave at the time t₀ to the j^th interfered wave at the time t.