A wavefunction with this shape is the propagator of the diffusion equation. The normalizable solution to the Schrödinger equation for a free particle is typically assumed to be a wavefunction with this shape. Because the Fourier transform of a wavefunction with this shape also has this shape, those wavefunctions satisfy the lower bound of the uncertainty principle. A wavefunction with this shape is the ground state of the quantum harmonic (*) oscillator. Uniquely, "spreading" wavepackets with this shape maintain this shape as they propagate, with their width "sigma-x" growing linearly in time. The idealized output of a laser is a beam whose intensity profile is this distribution, which is proportional to "e to the negative x-squared." For 10 points, name this waveform that is normally distributed about a mean. ■END■
ANSWER: Gaussian [or bell curve; accept normal distribution until read; accept Gaussian wavepacket]
<BW, Physics>
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