It relates the number of bound states of a potential to the difference in phase of a scattered wave at zero and infinite energies.
12.
Such flaws are detected when they reflect or scatter the impinging wave and the reflected or scattered wave reaches the search unit with sufficient amplitude.
13.
If a change occurs, such as a crack in the medium, the change in the multiple scattered waves will result in an observable change in the coda waves.
14.
In the Born approximation the amplitude of the scattered wave corresponding to the scattering vector \ mathbf { q } is proportional to the Fourier transform \ textstyle \ psi ( \ mathbf { q } ).
15.
His brain barely functions _ not enough for his eyes to blink, for his lungs to inflate and deflate on their own or for his throat to swallow food, but enough to make scattered waves on a scan.
16.
One path to the reciprocal lattice of an arbitrary collection of atoms comes from the idea of scattered waves in the Huygens-style sum of amplitudes from all points of scattering ( in this case from each individual atom ).
17.
We therefore expect \ Psi _ { \ mathrm { s } } ( \ mathbf r ) \ propto \ exp ( ikr ) / r at large distances and set the asymptotic form of the scattered wave to
18.
In order for Rayleigh's model to apply, the sphere must be much smaller in diameter than the wavelength ( " ? " ) of the scattered wave; typically the upper limit is taken to be about 1 / 10 the wavelength.
19.
Initially, the primary benefit seen to be offered by radar imaging was its capability for operating at night and also for imaging through clouds or other atmospheric obstructions which absorbed or scattered waves not only in the visible spectrum but also in the nearby infra-red and ultraviolet.
20.
Since the lattice points are displaced by the Bravais lattice vectors, \ scriptstyle \ mathbf { R }, scattered waves interfere constructively when the above condition holds simultaneously for all values of \ scriptstyle \ mathbf { R } which are Bravais lattice vectors, the condition then becomes:
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