meta user
network profile
| bio | website | |
|---|---|---|
| location | Kolkata,India[91-33-25514464] | |
| age | ||
| visits | member for | 1 year, 6 months |
| seen | Mar 27 at 12:06 | |
| stats | profile views | 225 |
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 added 177 characters in body |
|
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? |
