What is Wave packets: Definition and 36 Discussions

In physics, a wave packet (or wave train) is a short "burst" or "envelope" of localized wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere.
Each component wave function, and hence the wave packet, are solutions of a wave equation. Depending on the wave equation, the wave packet's profile may remain constant (no dispersion, see figure) or it may change (dispersion) while propagating.
Quantum mechanics ascribes a special significance to the wave packet; it is interpreted as a probability amplitude, its norm squared describing the probability density that a particle or particles in a particular state will be measured to have a given position or momentum. The wave equation is in this case the Schrödinger equation. It is possible to deduce the time evolution of a quantum mechanical system, similar to the process of the Hamiltonian formalism in classical mechanics. The dispersive character of solutions of the Schrödinger equation has played an important role in rejecting Schrödinger's original interpretation, and accepting the Born rule.In the coordinate representation of the wave (such as the Cartesian coordinate system), the position of the physical object's localized probability is specified by the position of the packet solution. Moreover, the narrower the spatial wave packet, and therefore the better localized the position of the wave packet, the larger the spread in the momentum of the wave. This trade-off between spread in position and spread in momentum is a characteristic feature of the Heisenberg uncertainty principle,
and will be illustrated below.

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  1. F

    I Does mean velocity equal group velocity of wave packets in QM?

    Does mean velocity of particle equal group velocity of wave packet in QM?If they do not equal which of them is classical velocity?
  2. X

    Normalizing wavefunction obtained from Lorentzian wave packet

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  3. S

    Average speed of a probability density wave and wave packets

    Show that ##v_{av}=\frac{\hbar k_2 + \hbar k_1}{2m}## is equal to ##v_{av}=\frac{\omega_2 - \omega_1}{k_2-k_1}##. Which of the identities listed above (if any) would make the sign change between ##k_2## and ##k_1##? One can attain a "wave packet" by superposing two or more sinusoidal waves...
  4. I

    I Instantly reformable wave packets instead of "particles"?

    Hello, I am a high school physics teacher, and I have been thinking about a way to model quantum mechanics in an intuitive way in order to teach it better, but I don't want to lead my students down the wrong path. I am certainly no expert in quantum theory. In looking at the guidelines, I...
  5. E

    I Question about photon wave packets

    Has anyone ever tried to measure the number of waves in photon wave packets? It seems like that would be an important feature and would be equal to the number of fringes in the double slit experiment (on one side), unless it is a huge number. Also, the decrease in the intensity of fringes as...
  6. D

    I Finding expansion coefficient of a 3-d Gaussian wave packet

    I'm having trouble with trying to find the expansion coefficients of a superposition of a Gaussian wave packet. First I'm decomposing a Gaussian wave packet $$\psi(\textbf{r},0) = \frac{1}{(2\pi)^{3/4}\sigma^{3/2}}\text{exp}\left[ -\frac{(\textbf{r} - \textbf{r}_0)^2}{4\sigma^2} + i\textbf{k}_0...
  7. Safder Aree

    Wave packet width given a wave function

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  8. LarryS

    B Do wave packets really represent a free particle?

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  9. Elvis 123456789

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  10. RicardoMP

    I What is the width of a wave packet?

    I'm reading Gasiorowicz's Quantum Physics and at the beggining of chapter 2, SG introduces the concept of "wave packet" and gaussian functions associated to them. The first attached image is the 28th page of the book's 1st edition I suppose, and my question is about the paragraph inside the red...
  11. anorlunda

    Dirac on Spreading Wave Packets

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  12. V

    Quantum Physics: Gaussian Wave Packets

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  13. J

    Understanding Wave Packets in Quantum Physics

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  14. D

    Can quantum operators be pictured in terms of wave packets?

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  15. M

    What does propogation of wave packets mean?

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  16. H

    Understanding Group Velocity for Wave Packets in a 1-D Particle in Box

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  17. P

    Uncertainty Relations & Wave Packets

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  18. L

    Simple wave packets problem

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  19. N

    How fast do wave packets typically spread out?

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  20. W

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  21. R

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  22. C

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  23. E

    Minimum uncertainty wave packets energy interpretation

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  24. R

    Phase velocity wave packets Modern Physics

    Homework Statement The phase velocity of each wavelength of white light moving through or- dinary glass is a function of the wavelength i.e. glass is a dispersive medium. What is the general dependence of phase velocity on wavelength in glass? Is dvp/dlamda positive or negative? Why...
  25. LarryS

    Gaussian Wave Packets - Fiction?

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  26. A

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  27. T

    Time Evolution of Gaussian Wave packets

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  28. H

    Gaussian Wave Packet: Reflection & Transmission

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  29. L

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  30. O

    Is entanglement just a mathematical construct or is it a real phenomenon?

    Hi, In some books and sites it's said to be nothing but physical wave packet for physical particles. They says a real-physical wave packet can exhibit all the features of a massive particle. Is it true(shown with experiments?), or is it one of the interpretations?
  31. L

    Is the Size of a Wave Packet Constant in Quantum Physics?

    Hello: I need some help with a homework problem that was taken from Quantum Physics by Gasiorowicz. The problem goes like this: You have a beam of electrons and know the size of the wave packet, and by the uncertainty principle you can estimate the dispersion in p at t=0. The problem is to...
  32. H

    Why Do We Need Wave Packets in Water Waves?

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  33. J

    Wave packets that feel harmonic potential

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  34. wolram

    Unraveling the Mystery of Wave Packets: Manufacturing the Universe

    I do not know if this is the correct modern term, but it seems that particles can be thought of as wave packets? no matter what they are, what is manufacturing these packets in such a way that our universe is as we see it?
  35. H

    How Are Group Velocity and Phase Velocity Related in Wave Packets?

    Wave packets has a group velocity of v_{group}=\frac{d\omega}{dk} and its phase velocity is v_{phase}=\frac{\omega}{k} Show that the group velocity and the phase velocity are related by: v_{group} = v_{phase} - \lambda\frac{dv_{phase}}{d\lambda} Can someone please tell me...
  36. K

    Can the path integral method explain the spreading of wave packets over time?

    Why does a wave packet spread out in space as time passes? What difference would it make to the universe if it did not? And have a look at this link which shows a movie of "the time evolution of a quantum wave packet." http://webphysics.davidson.edu/mjb/acs_transformations_qm/packet.html...
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