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Results tagged with dirac-delta-distributions
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user 83398
Distributions are generalized functions, such as, e.g., the Dirac delta function. DO NOT USE THIS TAG for statistical probability distributions, profiles, graphs, plots, etc.
5
votes
Accepted
What are the dimensions for the Heaviside Step Function?
The step function is dimensionless. We can immediately see this using its basic definition. We can also see it using the distribution definition,
$$\int H(x) \phi'(x) dx = -\phi(0).$$
The dimensions o …
- 105k
8
votes
Accepted
Question on doing the integral for Fermi golden rule
The delta function $\delta(x)$ has unit area, but the function $\delta(2x)$ is "half as wide" and thus has half as much area; thus you can pick up extra factors from 'how fast' you cross the peak of t …
- 105k
2
votes
How to define the light "color" from a given spectral distribution?
Unfortunately, since color is a matter of perception, this is almost purely a biology question. The problem is that, while we perceive sound rather faithfully (our ears basically just do a Fourier tra …
- 105k
13
votes
Accepted
Is $\delta(r-ct)/4\pi r$, the 3D wave equation elementary solution, a transverse or longitud...
The question doesn't make sense, since the terms "transverse" and "longitudinal" don't apply to scalar fields. They refer to the relationship between the polarization of a wave and its propagation dir …
- 105k
3
votes
Accepted
Confusing derivations of Planck's Law in different books
All of your sources are correct.
The Boltzmann distribution states that the probability of a single state being occupied is proportional to $e^{-E/kT}$.
To get the probability of a range of energi …
- 105k
2
votes
Why does the S matrix always contain a factor of $(2\pi)^4?$
Just remember the standard good $2 \pi$ conventions:
every time you have any integral over momentum, put the $2\pi$ in the denominator, $d^dp / (2 \pi)^d$
every time you have a delta function of mom …
- 105k
3
votes
Accepted
Triple Delta Potential in Quantum Mechanics
From here, a simple sketch of the potential highlights $4$ regions:
$$\begin{cases}
x < -a \\
-a < x < +a\\
a < x < 2a \\
x > 2a
\end{cases}
$$
This is wrong. A delta function $\delta(x + x_0)$ …
- 105k