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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?
Aug
21
asked Is it Possible to have Adiabatic Processes other than $PV^\gamma$ for the ideal Gas?
Aug
20
revised Do processes $P\propto\frac{1}{V^2}$, $P\propto\frac{1}{V^3}$, $P\propto\frac{1}{V^4}$, etc., exist in the real world?
added 73 characters in body
Aug
20
answered Do processes $P\propto\frac{1}{V^2}$, $P\propto\frac{1}{V^3}$, $P\propto\frac{1}{V^4}$, etc., exist in the real world?
Aug
20
comment On the Discretization of Energy Levels
A measurement performed on the state of a system is an $operation$ on the system intended to obtain a value for some physical quantity. For measuring different physical quantities we need to perform, in a natural way, different types of measurement to be represented by distinct $operators$. This commonsense idea is in tune with the formal technique in QM:Operator acting on the $\psi-function$ generates the eignvalues,ie, the numbers used to denote specific physical properties.
Aug
19
comment On the Discretization of Energy Levels
$\sigma_x \sigma_y=\frac{Cov(X,Y)}{\rho} greater{\;} than{\;} zero$. I have written it here since in my previous comment the greater than sign is looking like a right arrow.How do you write greater than in Latex?(I know how to write greater than equal to in latex,\ge?
Aug
19
comment On the Discretization of Energy Levels
Edit :1.$Cov(X,Y)=\rho{\;} \sigma_x \sigma_y $ 2.We have,$\sigma_x \sigma_y=\frac{Cov(X,Y)}{\rho} > 0$ if the variables X and Y have some dependence. 3.For a precise measurement I have implied X=const or Y= const . For such a situation we have $Cov(X,Y)=0$ and the variables lose their dependence or association.
Aug
19
comment On the Discretization of Energy Levels
Uncertainty Principle from the Classical Ideas:$[Cov(X,Y)]^2=\rho^2 \sigma_x \sigma_y$. X ans Y are two variables that have an association with each other for example the position coordinate $x$ and momentum $p_x$ in the process of a measurement $Cov(x,y)\ne 0$ implies $\sigma_x \sigma_y \ne 0$ that is,$\sigma_x \times \sigma_y=\frac{Cov(X,Y)}{\rho^2}= A{\;\;}positive{\;\;} Quantity$.For a precise measurement of X or Y $Cov(X,Y)=0$ leading to an independence of the two variables concerned.The above classical facts indicate towards an uncertainty relation
Aug
18
comment Do processes $P\propto\frac{1}{V^2}$, $P\propto\frac{1}{V^3}$, $P\propto\frac{1}{V^4}$, etc., exist in the real world?
You can always connect a pair of points$(P_1,V_1)$ and $(P_2,V_2)$ on the P-V indicator diagram by some arbitrary continuous path.Each infinitesimal element of this path may be decomposed into an isothermal and an adiabatic component to visualize the thing,a standard technique.
Aug
18
comment On the Discretization of Energy Levels
You may think in terms of the Fourier decomposition of a particular function represented by the oscillating string.For a physical problem the constant coefficients in the Fourier series should be of reasonable values so that the series does not blow up. You may have an infinite number of terms(modes) leading to a finite values of energy for the system
Aug
18
comment On the Discretization of Energy Levels
Let's consider the example of a string stretched between a pair of fixed points. You may pluck the string at some point suppressing a multitude of modes. Still you have an infinite number of modes left in the oscillation. Do the highest or rather the higher frequency modes have as large an amplitude as the fundamental?
Aug
18
comment On the Discretization of Energy Levels
Let's go into a simple treatment:The number of modes of frequency $\nu_n$ for the first octant of a sphere of radius "n":$N=\frac{1}{8}\frac{4\pi}{3} n^3=\frac{\pi}{6}(\frac{2L}{c})^3 \nu_n^2$---(1)Therefore number of modes on the interval$(\nu_n,\nu_n+d \nu_n)$:$dN=\frac{4\pi}{c^3}L^2{\mu_n}^2 d\mu_n$. N and dN correspond to possible modes and not to the actual modes that may be realized consistently if the energy of the system ,its total momentum etc remain unchanged.These factors asre considered in the derivation of the Maxwell -Boltzman distribution.
Aug
18
comment On the Discretization of Energy Levels
Maxwell' Boltzman's Distribution is a unimodal bell shaped one assigning the highest probability to the mean speed of the entire system of oscillators at least in an approximate way.The mean speed of the highest frequency oscillator is much greater than the said mean value pertaining to the entire mass of oscillators.Any effort to assign the largest strength to the oscillators on the higher frequency side would be a big mistake even from the classical point of view. Maxwellian distribution of momenta,incidentally, remain valid even in a potential field.
Aug
18
revised On the Discretization of Energy Levels
added 281 characters in body
Aug
18
comment On the Discretization of Energy Levels
Just think of a pair of particles participating in an elastic collision.You don't get arbitrary solutions satisfying the equations involved.Now you may extend your thinking to ten particles and then to ten million particles involved in an elastic collision(net force on the system being zero). The relaxation time and its constant nature become important when you are considering a huge number of particles.
Aug
18
asked On the Discretization of Energy Levels