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210
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location Kolkata,India[91-33-25514464]
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visits member for 2 years, 5 months
seen Mar 27 '13 at 12:06

Author/Teacher from India. Interested in General Relativity and other areas of physics


Sep
7
comment Counterpart of the Klein Gordon Equation on the “Coordinate Shell”
$\frac{\partial E}{\partial t}=\frac{\partial E}{\partial \psi}\frac{\partial \psi}{\partial t}$Or,$\frac{\partial^2 E}{\partial t^2}=\frac{\partial^2 E}{\partial \psi^2}(\frac{\partial \psi}{\partial t})^2+\frac{\partial E}{\partial \psi}\frac{\partial^2 \psi}{\partial t^2}$Similarly:$\frac{\partial^2 E}{\partial x^2}=\frac{\partial^2 E}{\partial \psi^2}(\frac{\partial \psi}{\partial x})^2+\frac{\partial E}{\partial \psi}\frac{\partial^2 \psi}{\partial x^2}$ We finally have$\frac{\partial^2 E}{\partial t^2}-\frac{\partial^2 E}{\partial x^2}=0$ for points where mass=0.
Sep
7
revised Counterpart of the Klein Gordon Equation on the “Coordinate Shell”
added 162 characters in body
Sep
7
comment Counterpart of the Klein Gordon Equation on the “Coordinate Shell”
As the $\psi$ wave passes through a point the values of energy and momentum(determining the spacetime curvature) can change in a specific manner as given by PDE(2) if we are to stay on the "coordinate shell"
Sep
7
revised Counterpart of the Klein Gordon Equation on the “Coordinate Shell”
added 2 characters in body
Sep
7
revised Counterpart of the Klein Gordon Equation on the “Coordinate Shell”
added 12 characters in body
Sep
7
comment Counterpart of the Klein Gordon Equation on the “Coordinate Shell”
I have used the term analogue/counterpart in the sense that the variables get interchanged,for example E<-->t;p(x)<---->x etc. We get the wave equation[speed=c=1] with the variables interchanged.
Sep
7
asked Counterpart of the Klein Gordon Equation on the “Coordinate Shell”
Sep
1
awarded  Enthusiast
Aug
27
revised On the Discretization of Energy Levels
added 335 characters in body
Aug
27
revised On the Discretization of Energy Levels
added 92 characters in body
Aug
26
comment On the Discretization of Energy Levels
We may write directly,$F(E,P)=\int_{\infty}^{-\infty}\int_{\infty}^{-\infty}f(x,t)e^{ia(Et-px‌​)}dxdt$ and use the facts $\frac{\partial F}{\partial x}=0$ and $\frac{\partial F}{\partial x}=0$ to arrive the results in the previous comments.
Aug
26
comment On the Discretization of Energy Levels
Regarding Relation B in the scond last comment:(1) It satisfies the Klein Gordon Relation. (2)For the invariance of the exponential part the Lorentz transformations are a suitable candidate provided "a" is a universal constant.(3)Energy and momentum are suitable choices for E and p if Et and px are dimensionally identical.(4)The psi indicated by relation (B)is periodic nature associated with a probability picture.
Aug
26
comment On the Discretization of Energy Levels
Relation (A) becomes the Fourier transform when both x and t tend to infinity.Using (B) in (A) and allowing x and t to tend to $\infty$,we obtain:$F(E,p)=Const\times \delta(E-E_0)\delta(p-p_0)$ Integration of the last formula on the (E,p) domain counts the number of (E0,p0) modes present.If we divide this by the total number of possible modes we obtain a probability picture
Aug
26
comment On the Discretization of Energy Levels
$F(E,p,x,t)=\int_{-\infty}^{x}\int_{-\infty}^{t}f(x,t)e^{ia(Et-px)}dxdt$----(A).‌​$\frac{\partial F}{\partial x}=\int_{-\infty}^{x}\int_{-\infty}^{t}(\frac{\partial f}{\partial x}-ipxf)e^{ia(Et-px)}$ Again $\frac{\partial F}{\partial x}=\int_{-\infty}^{x}\int_{-\infty}^{t}(\frac{\partial f}{\partial t}-iEf)e^{ia(Et-px)}$. If $\frac{\partial F}{\partial x}=0$ favors $\frac{\partial f}{\partial x}-iap=0$ =>$(x,t)=Ae^{iapx}$. Again, $\frac{\partial F}{\partial x}=0$ should favor $f(x,t)=Be^{-iaEt}$. Finally we obtain $f(x,t)=Ae^{-ia(Et-px)}$--(B)which is a solution of the Klien Gordon equation.
Aug
25
comment On the Discretization of Energy Levels
A Relevant Paper:independent.academia.edu/AnamitraPalit/Papers/1889577/…
Aug
22
revised On the Discretization of Energy Levels
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Aug
21
comment Pseudo-Superluminal Motion and the Synchronization of Clocks
@RonMiamon:Observers at A and B agree that the speed of light locally is "c" : that is OK. But if you think of a light ray passing over a finite distance from A to B the average speed of light measured by the observer at A (or at B) = distance of separation(physical)/Time measured by his own clock. And this value may be different from "c"
Aug
21
accepted Pseudo-Superluminal Motion and the Synchronization of Clocks
Aug
21
awarded  Scholar
Aug
21
accepted Is it Possible to have Adiabatic Processes other than $PV^\gamma$ for the ideal Gas?