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Bernard
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Trivial question: If a wave-packet is spreading with time, should the width of the wave-packet grow linearly with time?
Not so trivial as the answer depends on the form of the wavepacket itself as well as the Hamiltonian operator.Bernard said:Trivial question: If a wave-packet is spreading with time, should the width of the wave-packet grow linearly with time?
A stationary wave packet is a quantum mechanical wave function that is localized in space and does not change over time. It is characterized by its width, which is a measure of the spread of the wave packet.
The width of a stationary wave packet is related to time through the Heisenberg uncertainty principle, which states that the more precisely the position of a particle is known, the less precisely its momentum can be known. As the wave packet evolves over time, its width will change accordingly.
The width of a stationary wave packet is affected by several factors, including the initial width of the wave packet, the potential energy of the system, and the mass of the particle. These factors can cause the wave packet to spread out or become more localized over time.
Yes, the width of a stationary wave packet can be measured experimentally using techniques such as time-of-flight measurements or diffraction experiments. These measurements can provide information about the evolution of the wave packet over time.
The width of a stationary wave packet is important in quantum mechanics because it provides information about the uncertainty in the position and momentum of a particle. It also plays a crucial role in understanding the behavior of quantum systems and their evolution over time.