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fxdung
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Does mean velocity of particle equal group velocity of wave packet in QM?If they do not equal which of them is classical velocity?
##m \times## the expectation value of ##k##, the Fourier transform of ##x## ?fxdung said:Sum of v*probability of given v
In quantum mechanics, mean velocity refers to the average velocity of a single particle, while group velocity refers to the velocity of a group of particles or a wave packet. Mean velocity takes into account the position and momentum of a single particle, while group velocity considers the collective motion of a group of particles.
In quantum mechanics, mean velocity is calculated using the expectation value of the momentum operator. This is done by taking the integral of the momentum operator with respect to the wave function, and dividing by the integral of the wave function squared.
The uncertainty principle in quantum mechanics states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. This is also true for wave packets, where a more localized wave packet will have a larger uncertainty in momentum, resulting in a smaller group velocity.
Yes, mean velocity and group velocity can be different in quantum mechanics. This is because mean velocity takes into account the properties of a single particle, while group velocity considers the collective motion of a group of particles. In certain cases, such as with wave packets, the two velocities may differ due to the uncertainty principle.
The concept of mean velocity and group velocity is important in understanding various phenomena in quantum mechanics, such as the behavior of electrons in a solid or the propagation of light in a medium. It also has applications in technology, such as in the development of quantum computers and communication systems.