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International Journal of Physics and Research (IJPR) ISSN 2250-0030 Vol. 3, Issue 4, Oct 2013, 43-54 © TJPRC Pvt. Ltd.

THEORY ON SCHRÖDINGER CLOUD EQUATION SUGATO GHOSH Calcutta Institute of Technology, Uluberia, West Bengal, India

ABSTRACT I performed quantum Schrödinger cloud equation with the progressive properties of wave function and interpretation of wave cloud function. From the fundamental Schrodinger wave equation I derived the cloud wave function which is being propagate wave as a function of energy transfer with its decoherence stage .Source of generating wave function are in a random motion of a particle with any direction ,starting from any point generated a S-P line wave function and these generation creates a wave propagation in geometrical elliptical space with pulse transformation with low decoherence value of high amplitude and it transverse pulse on the space region with visualistic sin wave function. The high decoherence low microwave propagate a pulse in the vacuue weak space of the ellipse and coherence of wave propagation in the shift space wave transformation or, when the two pulse of microwave merge together in the occupied space it transfer with constant amplitude with constant wave pulse propagation. The beneficial effect of low decoherence weak vacuue space of ellipse without the sin wave propagation as an experimental set up for determination of an atom optical wave dimension in weak decoherence stage of atom in space boundary regime.

KEYWORDS: Schrodinger Cloud Equation, Sugato Pulse INTRODUCTION Quantum mechanics with fundamental of L de Broglie [1]on what he called “phase wave “ (“ondes de phase “ ) and thought to be associated with the motion of material points , especially with the motion of an electron or proton . Later E. Schrödinger [2] determine the wave function physically means and determine a continuous distribution of electricity in space, the fluctuation of which determine the radiation by the law of ordinary electrodynamics, non-conservation system , theory of dispersion and scattering and the ‘transition’ between the ‘stationary states’. Based on these the wave propagation in ‘quantum beats’ detection in spectroscopic techniques in which use is made of pulsed character [3]. With integrate the fundamental tests of quantum mechanics have been performed on the system, include the first detection of field quantum jumps [4,5] and later quantum measurement theory , to be use QND method to prepare non –classical fock and Schrodinger cat state of the field and to reconstruct their Winger function [6] under the functional evolution and direct observation of the decoherence process[7] . In the state of decoherence ,microwave propagate, in these field with coherence growth with 3-D wave propagation in the ellipse space in strong and weak L p [8] path of the space region and scattered the wave, during interchangeability of space shift , phase propagate pulse wave in the thin coherent zone.

DERIVATION OF THE SCHRODINGER CLOUD EQUATION The wave decoherence state propagation take place in space with the particle wave function of two coherence stage of truth. The wave propagation with boundary condition in time independent Schrodinger equation with V(x) potentiality is = And time independent wave potentiality

(1)


44

Sugato Ghosh

=

(2)

For the free particle. But the function with time or without time does not give a Regulatic pulse wave in the space regime and it does not give a pulse wave in s-p line in the random motion (Brownian motion) particle. In space so as we take a least square function with utility to state of decoherence wave generation with the unit single value wave function with the boundary barriers. The wave amplitude is in a condition with high amplitude with low decoherence stage and low amplitude with high decoherence stage. Now considering with constant sphere of space universe, we take the energy E=h Ϣ but due to shift phase rotating universe it‘s energy coherence ratio

=

, where γ as a function of the scattered photon per shift

phase position [10].Recurrence generating energy pulse to the surrounding and these pulse waves Energy function (1+ E) n

a binomial series of the coherent energy field amplitude with the finite phase wave transformation in decoherence energy

state. 1+

+ ………+

+

(3)

We take a single spin atom as earth planet in a reference static frame ,earth energy growth in space geometry, we take on

=

=

where

is radiant energy quanta and Ea absorbing energy quanta in space .It is a supermative space

energy equation for universe. Neglecting, 1+ higher order terms for infinite number of Energy growth in decoherence stages. Reconstruct the wave propagation in S-p line to the random wave motion in the decoherence stage; we set the wave propagation in non dimensional wave growth with unit wave velocity propagation. So as =1 /

=1

(4) (5) (6)

E= (

)/

) +2V

(7)

In decoherence stage the single wave having two coherence pulse generated in spin atom, the wave function are time dependent, time independent in a concentric circle, due to string gravity the center point of circle being shifted with a second focus with the eccentric value <1 the shift center become a ellipse orbitic rotation, and hence,(-

, 0 ) is the

center of ellipse .The wave equation +

=1

(8)

And the quadratic function of h is -

μ-

=0

(9)


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Theory on Schrödinger Cloud Equation

Where μ = The roots of the equation =

and

=

(10)

On the above wave equation, the nature of roots is sin wave curve as visualistic light wave which are either a constant pulse or an incrementing or decrementing pulse of an ellipse that pulse in the ellipse with either constant dire tic or varying dire tic length . But the occurrences of the discontinuity parallel wave line due to the weak pulse in the vacuue space of elliptical path are the shift phase pulse though either constant pulse or varying pulse generates ellipse boundary line. propagating pulse being a high energy decoherence stage .From the above equation of ellipse we generate the quadratic equation of pulse h as a functional equation with having two distinct root of amplification

, in a larger scale

we take a spin atom surrounded circular ribbon, rap eared outside the periphery with the high energy value of wave vibration in the vacuue space, though the space is a dynamic motion in universe and give a pulse motion on the top of the surface region and bottom of the surface region although in top give pulse with high decoherence state and low decoherence state at the bottom region . When two ellipse are in coherent pulse, merge together due to the energy binding wave force ,it give four dense wavelength or the four distinct root of h, give to pulse wave propagation in an off diagonal matrix, it being directed a dense cloud say as Schrödinger cloud wave propagation . It is written as τ=

.

+curl grad

(11)

Where E1 and E2 are the energy value of two coherent state of neighbor ellipses. From the above equation, the wave cloud being propagate with the motion in coherence state, due to the varying energy label, the dense pulse being propagate in space and the shift interchangeability occurs. Due to interchangeability sequences of wave propagate with high microwave to the low microwave in the space vacuue and its propagation in the form of light wave as an optical decoherence stage.

THE QUANTIZATION OF ENERGY The wave propagation is function of Schrodinger cloud and generated equation and solves it for τ

. The

Schrodinger cloud wave equation with decoherence stage gives the probability wave interpretation with the regime of diagonal dense matrix element as a valued function and cloud wave dense function in normalizing condition =1

(12)

For all time t, for the particular trial solution introduced above =

(13)

The requirement that the normalization condition must hold gives on substituting for

the results (14)

=

=1

(15)


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Sugato Ghosh

Since the integral must be infinite; (unity in fact), we must have

or E

+,-) ⧝

In the order of the integral function the clouds decoherence is being as a function of converged finite value. In that diagonal matrix element the wave length of sin curve of the ellipse cloud give to the pulse of convergence and it give the first pulse wave to the sin wave pulse ,being propagate to the shift pulse transformation to the next sin wave with the condition of boundary energy decoherence stage. So as the wave ellipse high decoherence low amplitude are become wave to a straight line function and has attracted towards the high amplitude low decoherence and as soon as it touch the wave it become a dot point function and superposition of the optic sin wave with same energy value function.

CONTINUITY CONDITION OF SCHRODINGER CLOUD In the cloud propagation with having a potentiality, with shift transverse optic wave transmission with varying state of decoherence, with the varying amplitude to gain a potential Pulse to the cloud wave function has to be superposition of one cloud to another and give to pulse propagation to the vacuue decoherence stage to create a discontinuity of continuous flow potentiality well. Schrodinger cloud is in a nature to a micro-wave supermative phase transformation to give responses of finite potential gain.

BOUNDARY STATE AND SCATTERING STATES OF SCHRÖDINGER CLOUD The propagate wave are in the previous section being superposition to give a finite potential. We have a definite energy E has a wave pulse generation to the pulse wave in occupied space to a vacuue space generation with the necessity of the existence space regimes barriers. Supermative the quantum Schrödinger cloud theory. But the problem here has in vacuue space wave propagation not give as distinct pulse wave propagation with the finite functional value are in trap of dot point existence of superposition on the real value sin wave . So as the answer lies with two coherence of attraction with high decoherence, low amplitude wave are in travel in the vacuue space of the ellipse porn to distinct transfer pulse propagation to occupied space with the particle trivial vibration in non –linear path. The next coherence state of decoherence Schrodinger wave propagation in cavity zone space with the confined field with around 51 GHz [5] microwave resonance in the supper conducting mirror. For the last case the gain potentiality with v(x) or v (γ) with five dimension(x,y,z,γ,t) and we obtained the wave function under satisfied boundary condition with quatic quantum state of photo trace onto the space with pulse mirror image.

SOLVING SCHRODINGER CLOUD EQUATION WITH INFINITE ENERGY DECOHERENCE WELL Suppose we have taken a single particle of mass m confined to the region of Decoherence pulse at zero <x< decoherence pulse at high microwave) within the potential energy =0 where γ as a function of non-demolition photon distribution in vacuum space [10]. Bounded infinitely high potential barriers i.e. =⧝ to x<zero pulse and x>high microwave, the potential experienced by the particle in the V

=0 decoherence pulse at zero<x<decoherence pulse to high microwave


47

Theory on Schrödinger Cloud Equation

=⧝ x>> high microwave

(16)

x< zero pulse

(17)

In the regime for which the potential is infinite, the wave function will be a transmit wave with zero potentiality, for exactly the same reasons that it was set to a vacuue null zero decoherence stage. The zero probability distribution of particle is being finding with these regimes. There must be impose to the boundary condition when low decoherence high microwave are in flow to merge in next elliptical space with high decoherence low microwave in the regime of boundary condition. So, ψ (pulse zero) = ψ’ (high microwave pulse )

(18)

Mean while in these regime Decoherence pulse at zero < x< decoherence pulse at high microwave

(19)

With pulse wave with time dependent Schrodinger cloud τ=

.

+curl grad

(20)

To solve these, Take p1=

and p2=

, then it is functional wave with two implicit vector in a monotonic line integral function

which it have p1=active wave resonant pulse and p2

=

dummy resonant pulse or vice versa with having five constraint,

where x,y,z being take as a single value functional vector ,with other two variable function , by applying Denjoy-Youngs Saks theorem Curl F=

(21)

Is

Under the boundary regimes τ= p2p1(0,t,0)+p1p2(0,0,γ) +

+p1(

+p2

(22)

So, I derived Sugato Pulse wave Equation If a pulse resonates with two waves transmit ion active and dummy resonance acted as a real value number with line integral function occupied in a space, the active pulse being as a vector to give a half spin in real coordinate space and the other half as a imaginary coordinate in space although dam may pulse act as a constant. So, the equation become τ=

+i

+

+i

+P2

(23)

It is gradient of two ordinate with real value and imaginary value variable function, it gives the roots of equation is


48

Sugato Ghosh

(X1 ,X2)=

(24)

Where the superposition of real axis to the imaginary axis is pulse superposition. It is a trace image of same numerical value in imaginary plane. It is a trace image of same value in –i complex coordinate. In the region the thin coherent pulse regimes for which the potential in infinite, the wave cloud function will be a vibration resonance with a zero amplitude wave function and it is the coherent amplitude of fork dot wave in a straight line function and long distance discontinuity occurs.

Figure 1: Coherent Field Wave in Space Let Dot Vaccy Existence in Earth Position Shifted Space Wave Transformation with Permeability=1.2566x10-6and PO+3, f=1.165x103 In the space vaccy , set up an experimentally as a universe & shift phase separation due pulse growth as earth give a fork dot wave in space &it has to be , shifted the next position where rotating optic ribbon are scattered in the form of fiber optic bundle. line extension to Graphs with earth permissible factor 1.2566x10-6 and calorific value of water 1.165x103 as the functional wave pulse generated energy value in a regular tic space let starts with grid function of wave propagation scattered 0.002 to .014 in twine with a regular tic dark spectra, in mid-bet line space with maximum limit calorific value of water & light of scattered phase -1 to 1 permissibility, brake on to its calorific value of water .014. Plotted x varies earth enthalpy is demo nested. We will set as a zero and the zero probability of the particle being found these regimes. Thus, we must impose the boundary condition. Ψ(0)=ψ(L)=0

(25)

Meanwhile, in the regimes [Decoherence pulse at zero<x< decoherence pulse at high microwave], the potential vanished, so the time independent Schrödinger Cloud equation becomes τ= P2 P1 (0, 0, γ) +P1 P2 (0,t, 0)+

+

+

(26)

In non-tribunal equation with time independent function, to solve these roots of these equation It impose boundary condition First at x=[Decoherence pulse at zero<x< decoherence pulse at high microwave], So, that the solution is a

(27)


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Theory on Schrödinger Cloud Equation

Ψ (x)=

Sin ( kx) +

sin(i kx))

(28)

K=i We apply the boundary condition x=[decoherence pulse at high microwave ] give ψ( )=

sin(K(decoherence pulse at high microwave ))+

sin (i K (decoherence pulse at high microwave )) (29)

Which tells as either in which is not a useful solution (it say that there is no particle in the well decoherence stage in weak space region at all. Or else Sin (-i

)=0

(30)

This gives an equation for -i

=in

(31)

n= 0,(+,0)1,(+,0)2, We excluded the n=0 possibility as that would give as, once again Ѱ(x)=0 and we exclude the negative value of n as in coherent thin pulse in space with the combination of blue and green wave length in light as these will merely reproduce as a same set of solution λ (expected with opposite sign ) as the positive value due to decoherence growth superposition of pulse energy is high wave length low decoherence stage . Thus we have =

)

Where we have introduce a subscript, these lead to, on using energy growth equation is =

(32)

QUANTITY OF DECOHERENCE GROWTH We defined the quantity with decoherence regime. From [8] gives the space Lp(p>= 1) which are made up of the measurable function f, defined in a measurable set e , for which |f|p is sum able. Here the norm ||f|| is defined by ||f||=[

p

dx]1/p

(33)

We have ||f||=0 if and only if f(x)=0 almost everywhere in e , we agree not to distinguish between two functions equal almost everywhere , just as in the case of L2.Minkowsi’s inequality , or equivalently the triangle inequality, is valid for this norm . As we have seen, whenever p>1, and obviously also for p=1 and the limiting case p=⧝. As for this last case, we understand L⧝ the space of measurable functions which are bounded or almost everywhere to bounded function , and we defined the norm ||f|| in L⧝ to be the “ true maximum” of |f(x)|, that is, the smallest value of M for which |f(x)|< =M almost everywhere. The reason for considering this space as a limiting case of the Lp spaces is that on sets of finite measure, as is easily seen, the norms of f corresponding to different exponents p tend, as p

⧝ to the bound M considered.

To arrive at the idea of scalar product, it is necessary to considered, besides Lp , where 1/p+1/q=1 and therefore q=p/(p-1) , p=q/(q-1), in the limiting case p=1 and p=⧝ , we have q=⧝, q=1 .


50

Sugato Ghosh

To simplify we written as real space Lp of real valued function. We should define as an positive exponents p<1, as we define weak convergence in the space ellipse wave propagation in high decoherence space with small microwave propagation the space being convergence in the Lp , 1<=p<⧝ by the sequence {fn} in Lp convergence weakly to f in Lp if every g of the “conjugate “ space Lp, (fn,g)=

(34)

As in the positive exponents, q<1 in second space as also Lq real valued function. We define strong convergence in the space ellipse wave propagation in low decoherence space with high microwave propagation the space being convergence in the Lq , 1<=q<⧝ by the sequence {fn} in Lq convergence weakly to f in Lq if every g of the “ second conjugate “ space Lq, (gn,f)= Where L stands

=

is the cloud wave conjugation .Then we tell

that either [(fn,g)=

]or[(gn,f)=

]

(35)

merge between low decoherence high microwave to high decoherence low microwave and high decoherence low microwave to low decoherence high microwave with a thin coherent pulse , it pulse generated to the space and space generated to the pulse wave propagation . It leads to a set of solution of function wave propagation f,g .

THE FINITE POTENTIAL WELL OF SCHRÖDINGER CLOUD EQUATION The infinite potential wall in the Schrodinger Cloud state with the thin coherent growth with a valuable wave optic model, Science, with the minimum amount of fuse ion [9] in the vanderwall ion trapped with the spectral line perturbation in wave zone of Ryberg –Ryberg coupling are in the generation of spin flip life time in a cavity block experiment with high ionized gas as molecule are in the state of ambiguous wave scattered in the thin coherent growth. This model serves to describe very accurately the quantum character of such system within the state of decoherence a high microwave pulse being generated. It is a finite block set up as an experiment by excited the wave pulse in a space cavity with high ionization to be scattered to frock quanta ionization. The principal of particle scattered being emitted with repeated injection in a pulse wave particle .It gives a pulse to the space and space retreated a pulse to the particle. But, of course, any potential well is of finite depth and if a particle in such well has an energy with thin coherent growth, and if particle in such a well having high energy comparable to the boundary growth wave length in the elliptic path with low decoherence state being transfer a pulse wave transformation to the weak convergence decoherence energy barrier. Due to the pulse transformation the particle being shifted with high microwave propagation to low microwave propagation gives a dynamic motion in the vacuue space give to the pulse on the particle and there is the prospect of particle escaping from the thin coherent space region to low microwave propagation in ellipse vacuue. This is true both classically and quantum mechanically, though, as you might expect the behavior in the quantum mechanical case is not


51

Theory on Schrödinger Cloud Equation

necessarily consistent with our classical physics based expectation. Thus we now proceed to look at the quantum properties of a particle in a finite potential well.

Figure 2: Finite Potential Coherent Thin Well In the case, the potential will be of the form V(x)=0 Decoherence pulse at zero < x < decoherence pulse at high microwave =V x>= decoherence pulse at zero i.e. We have ‘lowered’ the infinite barriers to a finite value V. We now want to solve the time independent Schrodinger equation for the particle. To do this we recognize that the problem can be split up into three parts Decoherence pulse at zero< x< decoherence pulse at high microwave x>> decoherence pulse at zero, where the potential is once again v. Therefore, to find the wave function for a particle of energy E, We have to solve three equations, one for each of the region [(

)/

) +2V1][ (

)/

) +2V2] + curl grad [(

)/

) +2V1][ (

)/

) +2V2 ]

= 0 x<<decoherence pulse at zero [(

)/

) +2V1][ (

(36) )/

) +2V2]=0 decoherence pulse at zero

<x< decoherence pulse at high microwave [(

)/

) +2V1][ (

)/

) +2V2 + curl grad [(

)/

) +2V1] [ (

= 0 x>>decoherence pulse at high microwave

)/

) +2V2 ] (37)

The solution to these equation take different form depending on whether τ<V or τ>V, We shall considered the force case separately τ<V curl grad [(

)/

) +2V1

][ (

)/

) +2V2 ] = 0

(38)


52

Sugato Ghosh

In this case wave pulse propagation is seems to zero. With the boundary condition the wave vibration in the space to vacuue and vacuue space creates a microwave pulse transmission to high pulse time with nanosecond existence. τ> V [(

)/

) +2V1][ (

)/

) +2V2

]+ curl grad [(

)/

) +2V1 ][ (

)/

]= 0

) +2V2 (39)

i2h1h2( )2 +2V1((-i h1

+

)/ (t))+curl grad [i2h1h2(

)]/(Ѱ(t))

2

+4V1V2=0

P(-i2 P+ a1)=-C1

(40) (41)

It is differential equation of propagate wave pulse in two conjugate parallel line wave, among them one are in low decoherence high microwave pulse and another high decoherence low microwave pulse propagation, though it is a wave pulse propagation, due to nature ,one of them high energy microwave, another low energy microwave. In a eptic space the boundary wave reciprocate to low energy microwave due to the interchangeability of pulse transmission of superconductivity pulse transmission during the span of time of transmission of wave pulse to the vacuue space. The soft wave pulse act as a absorbing propagate wave in nature. In this model the boundary wave of ellipse reciprocated a dynamic motion, where as soft carry forward the phase shift from one position to other position.

Figure 3: Shift of Soft Microwave in Wave Dynamic We determine the quantized equation of cloud to being propagate with the P.I of the equation (36), the P.I. being quantized with coherent flip time with the decoherence growth with energy level to be rich to the optical dimension with the infinitesimal micro ½ spin of boson atom with the existence with high energy microwave pulse propagate as energy recourse to the particle.

SCATTERING FROM A POTENTIAL BARRIER OF SCHRÖDINGER CLOUD EQUATION Strong space of ellipse comes in contact to the weak space of ellipse due to interchangeability a pulse generated and due to inertia of the particle within in between that space hypothetical gives zero pulse and zero spin of the particle, but transfer pulse wave in the strong space region to weak space region the pulse wave of boson particle with have an optical dimension it have a spin of existence of space with -½ spin state to + ½ spin of existence, at that existence of particle wave give a scattered wave to the environment . Transmission of wave scattered of a particle give a scattered wave in the form of a high microwave to low microwave wave pulse and the existence of particle with the state of interchangeability ½ spin to -1/2 spin or -1/2 spin to +1/2 spin with the pulse inertia of wave . The existence of pulse wave with zero spins being as small instance of existence of particle, though the pulse wave transform a high energy to low energy or low energy to high energy it have an optical dimension with scattered wave and the epic of two soft space are being interchange to the strong space with absorbing energy by scattered microwave.


53

Theory on Schrödinger Cloud Equation

In the cloud equation (23) curl grad [(

)/

) +2V1

][ (

)/

) +2V2 ] = 0

(42)

is hypothetically and mathematically zero , although the curl function itself shift to pulse phase 2 to 1 , these shift transmibility scattered as zero spin of visualistic observation . So the actual occurrence shift curl vector are transmit wave in the state of 0to 01 or 01 to 02, so as the existence of optical dimension comprises two ½ spin in nature.

Figure 4: Sketch of Scattering Wave in Potential Barrier of Schrödinger Wave Cloud

CONCLUSIONS Schrödinger wave cloud is a propagated wave in an ellipse space with coherence of soft and strong space with decoherence state and it will be propagate microwave with pulse. In state of thin coherence state of ellipse a wave scattered in a boson particle with ½ spin existence with its emission.

REFERENCES 1.

L. De Broglie Ann physique 3, 22(1925)

2.

E . Schrodinger “an undulatory theory of the mechanics of atoms and molecules “14,664,(1926)

3.

S. Haroche “ investigation of Rydberg D state of sodium by quantum beat spectroscopy using pulsed dye , 1976 Sov.J.Quantum telctrom, 6397

4.

Gleyzee S, Kuhur S, Guerlin c, Berune J, Deleglish S, Hoff U.B., Brune M, RaimondJ.M and Haroche .S 2007 nature 446297

5.

Guerlin C, Bernu J, Deleglise S, Sayrin C, Gleyzes S , Kulur S , Bunue M, Raimond J-M and Haroche S 2007 nature 448889

6.

Deleglish S, Dotsenko I, Sayrin C, Berun J , Brune M , Raimond J.M , and S, haroche Nature 45510

7.

S Haroche, I Dotesenko ,S Deleglise, C Sayrin , X Zhou,S Gleyze, C Guerlin, S Kuhr, M Brune and J-M Riamond (2009) Manipulating and Probing microwave fields in cavity by quantum non-demolition photon counting Phys scr/T137/014014

8.

Day M.M The space Lp with 0<p<1 , Bulletin Amer Math loc 46 (1940)816-823

9.

J.M Raimond , G Vitrant and S. hroche 1981 J.Phy B at mol phy 14L655

10. S. Ghosh 2013 International Journal of physics and Research, ISSN :-2250-00


6 theory on schelgier full  

I performed quantum Schrödinger cloud equation with the progressive properties of wave function and interpretation of wave cloud function....