What is Wave packet: Definition and 116 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. S

    Find the wave function of a Gaussian wave packet

    In particular, i am solving part b. I pulled off a couple of formulas from a textbook, but I'm quite sure they are incorrect to apply here. Can anyone guide me? Below is my attempt.
  2. L

    How Does Pulse Duration Affect Frequency Spread in a Gaussian-Enveloped Laser?

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  3. phosgene

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  4. S

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  5. P

    What happens to a photon wave packet when half out of a moving device?

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  6. J

    Using given Fourier transform to find the equation for the wave packet.

    Homework Statement Any wavepacket can be obtained by the superposition of an infinite number of plane waves using the so-called Fourier integral or Fourier transform f(x,t) = \frac{1}{\sqrt{2\pi}} _{-\infty}\int^\infty A(k)e^{i(kx-\omega t)} dk Find at t=0 the representation of the...
  7. I

    Wave packet - Integration by parts

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  8. L

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  9. E

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  10. T

    Time Evolution Of A 1-D Gaussian Wave Packet Under The Gravitational Potential

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  11. Y

    Square shape wave packet spreading

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  12. J

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  13. A

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  14. K

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  15. B

    Wave Packet Expansion: Physical Reason & Conservation Laws

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  16. Z

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  17. N

    Probability Current: from plane wave to wave packet?

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  18. A

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  19. A

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  20. A

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  21. K

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  22. G

    Maths of GPS: Understanding Wave Packet Group Velocity

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  23. K

    Wave packet momentum wave function

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  24. Z

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  25. D

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  26. E

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  27. 1

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  28. TrickyDicky

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  29. B

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  30. P

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  31. V

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  32. Shackleford

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  33. S

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  34. Math Jeans

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  35. R

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  36. Amith2006

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  37. L

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  38. G

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  39. B

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  40. M

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  41. T

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  42. A

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  43. Y

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  44. I

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  45. M

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  46. Q

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  47. E

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  48. S

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  49. maverick280857

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  50. A

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