Post History
#3: Post edited
by
C-T
·
2024-03-07T10:08:31Z (10 months ago)
The Fourier transforms we use are- $$
- \tilde{f}(\mathbf{p}) =\int f(\mathbf{x})
- \ e^{-i\mathbf{p}\cdot\mathbf{x}} \ d^3x
- $$
- $$
- f(\mathbf{x}) =\int \tilde{f}(\mathbf{p})\
- e^{i\mathbf{p}\cdot\mathbf{x}} \ \frac{d^3p}{(2\pi)^3}.
- $$
- In physics, it is useful to compute the transform of $1/p^3$
- $$
- I=\int \frac{1}{p^3}\
- e^{i\mathbf{p}\cdot\mathbf{x}} \ \frac{d^3p}{(2\pi)^3}.
- $$
- But I have no idea what it even mean since the integral is not well-defined.
- Take the following Fourier transform conventions
- $$
- \tilde{f}(\mathbf{p}) =\int f(\mathbf{x})
- \ e^{-i\mathbf{p}\cdot\mathbf{x}} \ d^3x
- $$
- $$
- f(\mathbf{x}) =\int \tilde{f}(\mathbf{p})\
- e^{i\mathbf{p}\cdot\mathbf{x}} \ \frac{d^3p}{(2\pi)^3}.
- $$
- In physics, it is useful to compute the transform of $1/p^3$
- $$
- I=\int \frac{1}{p^3}\
- e^{i\mathbf{p}\cdot\mathbf{x}} \ \frac{d^3p}{(2\pi)^3}.
- $$
- But I have no idea what it even mean since the integral is not well-defined.
#2: Post edited
by
C-T
·
2024-03-07T10:07:50Z (10 months ago)
- The Fourier transforms we use are
- $$
- \tilde{f}(\mathbf{p}) =\int f(\mathbf{x})
- \ e^{-i\mathbf{p}\cdot\mathbf{x}} \ d^3x
- $$
- $$
- f(\mathbf{x}) =\int \tilde{f}(\mathbf{p})\
- e^{i\mathbf{p}\cdot\mathbf{x}} \ \frac{d^3p}{(2\pi)^3}.
- $$
I want to calculate the transfom of $1/p^3$- $$
- I=\int \frac{1}{p^3}\
- e^{i\mathbf{p}\cdot\mathbf{x}} \ \frac{d^3p}{(2\pi)^3}.
$$
- The Fourier transforms we use are
- $$
- \tilde{f}(\mathbf{p}) =\int f(\mathbf{x})
- \ e^{-i\mathbf{p}\cdot\mathbf{x}} \ d^3x
- $$
- $$
- f(\mathbf{x}) =\int \tilde{f}(\mathbf{p})\
- e^{i\mathbf{p}\cdot\mathbf{x}} \ \frac{d^3p}{(2\pi)^3}.
- $$
- In physics, it is useful to compute the transform of $1/p^3$
- $$
- I=\int \frac{1}{p^3}\
- e^{i\mathbf{p}\cdot\mathbf{x}} \ \frac{d^3p}{(2\pi)^3}.
- $$
- But I have no idea what it even mean since the integral is not well-defined.
#1: Initial revision
by
C-T
·
2024-03-07T10:06:25Z (10 months ago)
The Fourier transform of $1/p^3$
The Fourier transforms we use are
$$
\tilde{f}(\mathbf{p}) =\int f(\mathbf{x})
\ e^{-i\mathbf{p}\cdot\mathbf{x}} \ d^3x
$$
$$
f(\mathbf{x}) =\int \tilde{f}(\mathbf{p})\
e^{i\mathbf{p}\cdot\mathbf{x}} \ \frac{d^3p}{(2\pi)^3}.
$$
I want to calculate the transfom of $1/p^3$
$$
I=\int \frac{1}{p^3}\
e^{i\mathbf{p}\cdot\mathbf{x}} \ \frac{d^3p}{(2\pi)^3}.
$$