Tagged Questions

A unitary linear operator which resolves a function on $\mathbb{R}^N$ into a linear superposition of "plane wave functions". Most often used in physics for calcalating the response of a time shift invariant linear system as the sum of its response to time harmonic excitation or for transforming a ...

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1
vote
2answers
359 views

Finding $\psi(x)$ from Fourier modes [closed]

In quantum physics we've defined: $$ \psi (x) = \sqrt{ \dfrac{1}{2 \pi \hbar} } \int^{ \infty }_{-\infty } \phi (p) \exp \left( i \dfrac{px}{ \hbar} \right) dp $$ Now, $$a(k) \equiv \sqrt{ \hbar } ...
6
votes
3answers
2k views

Why is the bispectrum not commonly used in experimental physics?

Power spectra, coherence spectra, and linear transfer functions are ubiquitous tools of experimental physics. However, our instruments often retain small nonlinear effects which can contaminate ...
5
votes
3answers
2k views

What is the relation between position and momentum wavefunctions in quantum physics?

I have read in a couple of places that $\psi(p)$ and $\psi(q)$ are Fourier transforms of one another (e.g. Penrose). But isn't a Fourier transform simply a decomposition of a function into a sum or ...
3
votes
5answers
479 views

Does this statement make any sense?

I am asking this question completely out of curiosity. The other day, my roommate, by mistake, used 'Light year' as a unit of time instead of distance. When I corrected him (pedantic, much), he said ...
3
votes
1answer
1k views

How do I compute the eigenfunctions of the Fourier Transform? [closed]

I read today (ref) that the Continuous Fourier Transform has four eigenvalues: +1, +i, -1, and -i. Associated with each eigenvalue is a space of eigenfunctions: functions which retain their form ...
27
votes
6answers
3k views

Fourier transformation in nature/natural physics?

I just came from a class on Fourier Transformations as applied to signal processing and sound. It all seems pretty abstract to me, so I was wondering if there were any physical systems that would ...