8
votes
Accepted
Currently self-studying QFT and The Standard Model by Schwartz and I'm stuck at equation 1.5 in Part 1 regarding black-body radiation
It just a clever use of the geometrical series:
$$\frac{1}{1-q} = \sum_{j=0}^\infty q^j$$
which is valid for any real number $q<1$.
Here $q = e^{-E_n\beta} \equiv e^{-\hbar\omega_n\beta}$. As long ...
- 6,328
4
votes
Accepted
Probability of observing harmonic oscillator at a particular position
When dealing with continuous distributions, one should make difference between probability and probability density. Probability of hitting any specific point of a continuous distribution is zero, ...
- 37.4k
3
votes
Is it true that the Poynting theorem $P=E\times H$ is quite valid for DC circuits?
Yes, Poynting's theorem
$$-\frac{\partial u}{\partial t}=
\vec{\nabla}\cdot\vec{S}+\vec{J}\cdot\vec{E}$$
or, equivalently, in integral form
$$-\frac{\partial}{\partial t}\int_V u\ dV=
\oint_{\...
- 25.9k
2
votes
Electric Power and Energy
Total power produced is not a concept. It would be like asking for "total speed" of a car. You don't total rates. You could have an average speed over a period of time, but not a total.
...
- 33.7k
2
votes
Accepted
Moving body is collided with a spring system.Why there is a difference in maximum compressed distance for different observers?
Your derivation of the difference in compression between the two frames is incorrect; after all, in Galilean relativity, spatial distances between points at a given time are the same between all ...
- 37.2k
1
vote
Dispersion of $E$ and $p$
No, $∆E^2$ is not $2\Delta E$: $$E^2 = p^2c^2 + (mc^2)^2$$
$$\delta(E^2) = \delta(p^2c^2) + \delta [(mc^2)^2]$$
$$ 2E.\delta(E) = c^2(2p.\delta(p)) + 0$$
$$\delta(E) = \frac{pc^2}{E} \delta(p)$$
Hope ...
- 2,733
1
vote
Is it true that the Poynting theorem $P=E\times H$ is quite valid for DC circuits?
If something is stationary, it is a special case of being time-varying (with time derivative equals zero). So there is no need to repeat the proof of Poynting's theorem in the narrow sense of ...
- 7,114
1
vote
Accepted
How can we say potential or chemical energy is part of an object?
In a detailed microscopic model of a system of particles, we can distinguish energy of the microscopic EM field (EM energy), and the other energy (due to mass and kinetic energy of massive particles).
...
- 27.9k
1
vote
Non-Work energy conversion
Work is a more general concept than a force acting through a distance.
The mechanics branch of physics primarily addresses work for a point particle, or a rigid body, for which there is no change in ...
- 6,188
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