scholarly journals MASS CONVERTED FROM THE ENERGY OF MOTION

2021 ◽  
Author(s):  
Vishal Pandey
Keyword(s):  
Kinetic Energy ◽  
Nuclear Physics ◽  
Rest Mass ◽  
Motion Vector ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Theory Of Relativity ◽  
Vector Form ◽  
Rest Energy ◽  
Wide Range

In the General Theory of Relativity it is being introduced that the energy of motion is converted to the mass of that particle or matter or we can say that are interchangeable. It has a wide range use in the nuclear physics. The whole equation 𝑬 = 𝒎𝒄 𝟐 is a relativistic mass-energy equivalence and the term “mass” is also relativistic in nature. In special relativity, however, the energy of a body at rest is determined to be 𝒎𝒄 𝟐 . Thus, each body of rest mass m possesses 𝒎𝒄 𝟐 of “rest energy,” which potentially is available for conversion to other forms of energy. Here we initiated a equation from this if the Energy of motion has a vector form and it is in 3D space model as we know the energy of motion converted it to mass here we can do it by quantum mechanics. We think of that if the energy of motion is equal to the kinetic energy (time-independent equation from the Schrödinger equations) then we can solve the vector form of the energy and can find how much mass is being converted from the energy of motion(vector form). Here we have taken the kinetic energy from the Schrödinger equations not that from kinematics if we do then the speed of light will be equal to the velocity of that particle, which is violating the law of relativity thus I used the Schrödinger equations for simplicity .We got the equation and we have to do some calculation of the partial differentials and if the value of 𝑴′ is coming to be negative then the particle doesn’t exist and else we can find the mass converted and also the existence of that particle or matter of the universe. By this process, we can get the mass, the existence of matter/particle in this universe for that instance. We can use it if the energy is in the vector form and given some distance traveled in vacuum/air for some definite time we will get the desired result of mass.

scholarly journals MASS CONVERTED FROM THE ENERGY OF MOTION

2021 ◽  
Author(s):  
Vishal Pandey
Keyword(s):  
Kinetic Energy ◽  
Nuclear Physics ◽  
Rest Mass ◽  
Motion Vector ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Theory Of Relativity ◽  
Vector Form ◽  
Rest Energy ◽  
Wide Range

In the General Theory of Relativity it is being introduced that the energy of motion is converted to the mass of that particle or matter or we can say that are interchangeable. It has a wide range use in the nuclear physics. The whole equation 𝑬 = 𝒎𝒄 𝟐 is a relativistic mass-energy equivalence and the term “mass” is also relativistic in nature. In special relativity, however, the energy of a body at rest is determined to be 𝒎𝒄 𝟐 . Thus, each body of rest mass m possesses 𝒎𝒄 𝟐 of “rest energy,” which potentially is available for conversion to other forms of energy. Here we initiated a equation from this if the Energy of motion has a vector form and it is in 3D space model as we know the energy of motion converted it to mass here we can do it by quantum mechanics. We think of that if the energy of motion is equal to the kinetic energy (time-independent equation from the Schrödinger equations) then we can solve the vector form of the energy and can find how much mass is being converted from the energy of motion(vector form). Here we have taken the kinetic energy from the Schrödinger equations not that from kinematics if we do then the speed of light will be equal to the velocity of that particle, which is violating the law of relativity thus I used the Schrödinger equations for simplicity .We got the equation and we have to do some calculation of the partial differentials and if the value of 𝑴′ is coming to be negative then the particle doesn’t exist and else we can find the mass converted and also the existence of that particle or matter of the universe. By this process, we can get the mass, the existence of matter/particle in this universe for that instance. We can use it if the energy is in the vector form and given some distance traveled in vacuum/air for some definite time we will get the desired result of mass.

scholarly journals Time Decay for Nonlinear Dissipative Schrödinger Equations in Optical Fields

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Nakao Hayashi ◽  
Chunhua Li ◽  
Pavel I. Naumkin
Keyword(s):  
Lower Bound ◽  
Positive Root ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Time Decay ◽  
Large Initial Data ◽  
Initial Value ◽  
Optical Fields ◽  
Gauge Invariant ◽  
Dissipative Condition

We consider the initial value problem for the nonlinear dissipative Schrödinger equations with a gauge invariant nonlinearityλup-1uof orderpn<p≤1+2/nfor arbitrarily large initial data, where the lower boundpnis a positive root ofn+2p2-6p-n=0forn≥2andp1=1+2forn=1.Our purpose is to extend the previous results for higher space dimensions concerningL2-time decay and to improve the lower bound ofpunder the same dissipative condition onλ∈C:Im⁡ λ<0andIm⁡ λ>p-1/2pRe λas in the previous works.

scholarly journals Infinitely many positive solutions of nonlinear Schrödinger equations

2021 ◽  
Vol 60 (2) ◽  
Author(s):  
Riccardo Molle ◽  
Donato Passaseo
Keyword(s):  
Positive Solutions ◽  
Radial Symmetry ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

AbstractThe paper deals with the equation $$-\Delta u+a(x) u =|u|^{p-1}u $$ - Δ u + a ( x ) u = | u | p - 1 u , $$u \in H^1({\mathbb {R}}^N)$$ u ∈ H 1 ( R N ) , with $$N\ge 2$$ N ≥ 2 , $$p> 1,\ p< {N+2\over N-2}$$ p > 1 , p < N + 2 N - 2 if $$N\ge 3$$ N ≥ 3 , $$a\in L^{N/2}_{loc}({\mathbb {R}}^N)$$ a ∈ L loc N / 2 ( R N ) , $$\inf a> 0$$ inf a > 0 , $$\lim _{|x| \rightarrow \infty } a(x)= a_\infty $$ lim | x | → ∞ a ( x ) = a ∞ . Assuming that the potential a(x) satisfies $$\lim _{|x| \rightarrow \infty }[a(x)-a_\infty ] e^{\eta |x|}= \infty \ \ \forall \eta > 0$$ lim | x | → ∞ [ a ( x ) - a ∞ ] e η | x | = ∞ ∀ η > 0 , $$ \lim _{\rho \rightarrow \infty } \sup \left\{ a(\rho \theta _1) - a(\rho \theta _2) \ :\ \theta _1, \theta _2 \in {\mathbb {R}}^N,\ |\theta _1|= |\theta _2|=1 \right\} e^{\tilde{\eta }\rho } = 0 \quad \text{ for } \text{ some } \ \tilde{\eta }> 0$$ lim ρ → ∞ sup a ( ρ θ 1 ) - a ( ρ θ 2 ) : θ 1 , θ 2 ∈ R N , | θ 1 | = | θ 2 | = 1 e η ~ ρ = 0 for some η ~ > 0 and other technical conditions, but not requiring any symmetry, the existence of infinitely many positive multi-bump solutions is proved. This result considerably improves those of previous papers because we do not require that a(x) has radial symmetry, or that $$N=2$$ N = 2 , or that $$|a(x)-a_\infty |$$ | a ( x ) - a ∞ | is uniformly small in $${\mathbb {R}}^N$$ R N , etc. ....

scholarly journals On some classes of generalized Schrödinger equations

2020 ◽  
Vol 10 (1) ◽  
pp. 522-533
Author(s):  
Amanda S. S. Correa Leão ◽  
Joelma Morbach ◽  
Andrelino V. Santos ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Laplacian Operator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Stationary Problems

Abstract Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

scholarly journals N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 733
Author(s):  
Yu-Shan Bai ◽  
Peng-Xiang Su ◽  
Wen-Xiu Ma
Keyword(s):  
Exact Solutions ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Lax Pairs ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
The Given

In this paper, by using the gauge transformation and the Lax pairs, the N-fold Darboux transformation (DT) of the classical three-component nonlinear Schrödinger (NLS) equations is given. In addition, by taking seed solutions and using the DT, exact solutions for the given NLS equations are constructed.

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