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| bio | website | |
|---|---|---|
| location | Kolkata,India[91-33-25514464] | |
| age | ||
| visits | member for | 1 year, 7 months |
| seen | Mar 27 at 12:06 | |
| stats | profile views | 226 |
Author/Teacher from India. Interested in General Relativity and other areas of physics
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Aug 21 |
asked | Is it Possible to have Adiabatic Processes other than $PV^\gamma$ for the ideal Gas? |
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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 |
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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? |
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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. |
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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? |
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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. |
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Aug 19 |
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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 |
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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. |
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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 |
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Aug 18 |
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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? |
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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. |
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Aug 18 |
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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. |
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Aug 18 |
revised |
On the Discretization of Energy Levels added 281 characters in body |
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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. |
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Aug 18 |
asked | On the Discretization of Energy Levels |
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Aug 16 |
revised |
The Stern Gerlach Experiment Revisited added 938 characters in body |
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Aug 14 |
comment |
How does one prove:$\nabla(\vec{\mu_m}\cdot\vec{B})\cdot\vec{dr}=0$? $B_x$ and $B_y$ have been assumed to be zero individually in the above comment.Small non-zero values of $B_x$ and $B_y$ definitely changes the picture. What about B_z?It as not supposed to produce any acceleration in the z-direction directly through magnetic effects or indirectly through electrical forces! |
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Aug 14 |
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How does one prove:$\nabla(\vec{\mu_m}\cdot\vec{B})\cdot\vec{dr}=0$? Point to Observe:If $\vec{B}$ varies spatially only in the z direction,we may have electric forces only in the y-z plane and not in the z direction.(Initial electric field is assumed to be zero).This follows from the Curl B equation The model proposed will not produce any force in the z-direction initially.Magnetic force being normal to $\vec{B}$ will also be on the x-y plane. There will no force in the z direction --electrical or magnetic in nature. |
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Aug 14 |
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How does one prove:$\nabla(\vec{\mu_m}\cdot\vec{B})\cdot\vec{dr}=0$? Edit:For the above comment $\int \vec{E}\rho dV=\nabla(\vec{\mu_0}\cdot\vec{B})\cdot\vec{dr}$Integration should cover all the chage in the current loop. |
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Aug 14 |
comment |
How does one prove:$\nabla(\vec{\mu_m}\cdot\vec{B})\cdot\vec{dr}=0$? Magnetic force cannot perform work but electric field can do work.Such a field may result from the spatial variation of B from the curl B equation[comment to the answer may be considered] |
