# 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. ### Average value of components of angular momentum for a wave packet

I have typed up the main problem in latex (see photo below) It seems all such integrals evaluates to 0, but that is apparantly unreasonable for in classical mechanics such a free particle is with nonzero angular momentum with respect to y axis.
2. ### Fourier transform of wave packet

I am unsure if ##h(x,t)## really is a wave packet, but it looks like one, hence the title. Anyway, so I'd like to determine ##\hat{h}(k,t=0)##. My attempt so far is recognizing that, without the real part in the integral, i.e. ##g(x,t)=\frac{1}{2\pi}\int_{-\infty}^{\infty} a(k)e^{i(kx-\omega...
3. ### I Wave packet experimental detection

I know the wave function "collapses" when a measurement is made but still not satisfied with it
4. ### Normalize the Gaussian wave packet

For normalizing this wave function, I began by finding the complex conjugate of psi and then multiplied it with the original psi. Now what I am getting is A^2 integral exp(2cx^2-4ax) dx = 1 Now I am not getting how to solve this exponential term. I tried by completing the square method but it is...
5. ### A Dispersion of the wave packet over time

since, in order to view the shape changes in our wave packet we are presented with the taylor expansion of the frequency ω(k) = ω(k0) + (k − k0)dω/dk + 1/2*(k − k0)^2 (d^2ω/dk^2) we are told that only the third term that is the 1/2*(k − k0)^2 (d^2ω/dk^2) contributes to change in shape of the...

12. ### I What is a Gaussian Wave Packet?

Can anyone tell me what a Gaussian Wave Packet is? What happens to the atoms inside a Gaussian Wave Packet? Can more than one Gaussian Wave Packet Exist in the same place? Thank you,

41. ### Quantum physics: proving wave packet is normalized

Homework Statement Following gaussian wave packet: ## \psi (x)= \frac{1}{\sqrt{\sqrt{\pi a^2}}} e^{-\frac{x^2}{2a^2}}## Prove that this function is normalized. Homework Equations ## \int_{- \infty}^{\infty} |\psi (x)|^2 dx = 1## The Attempt at a Solution Is ## \frac{1}{\sqrt{\sqrt{\pi a^2}}}...
42. ### Movement of a wave packet of a free particle

In my course there's a chapter with the mathematical explanation to find the real expression and localisation of a free particle with the superposited wave function. The same is used to explain the movemement of a wave packet (which is a free particle). I've worked out almost all the math behind...
43. ### Physical meaning of a wave packet w/ respect to HUP&duality

I'm a QM noob/newb trying to understand the physical implication of a wave packet, in my mind it is something like this: On the x-axis there is displacement (vibration), probability on the y. I Imagine stretching and compressing the wave packet. When I stretch it out, the amplitude must...
44. ### Expansion coefficients of a wave packet

Homework Statement What are the expansion coefficients of a wavepacket \Psi (x) = \sqrt{\frac{2}{L}}sin \frac{\pi x}{L} in the basis Ψn(x) of a particle in a periodic box of size L? Homework Equations \Psi (r,t) = {\sum_{n}^{}} a_{n}(t) \Psi _{n}(r) The Attempt at a Solution \left \langle...
45. ### How Does a Wave Packet Represent a Free Particle in Quantum Mechanics?

If you solve TISE with V=0, you get a plane wave. This is not normalizable, so it's not a physically achievable state. But a linear combination does (?) I know why it does from the mathematics, a linear combination of plane waves is normalizable, but what does it really mean? A free particle is...
46. ### Gaussian Wave Packet: Solve Homework Equations

Homework Statement Wave function of an electron: ##\frac{1}{N}∫_a^b[e^{ik_0x}(1+\frac{1}{2}e^{i\frac{0.1}{2}x}+\frac{1}{2}e^{-i\frac{0.1}{2}x})]dx## The integrand becomes zero both to the left and right of x = 0 . Let a be the first time it hits zero to the left and b the first time it...
47. ### Wave packet with increasing time

I am trying to understand how a gaussian packet varies in time. Suppose we have a Gaussian wave packet that is displaced form the origin by an amount x0 and given initial momentum p0. So the wave function in coordinate space is ψ(x,0) =\frac{√β}{√√\pi}exp(-β2(x-x0)2/2)*exp(ip0x/ħ) where...
48. ### Definition of a Gaussian wave packet for a Initial State

Hi :) I'm reading a didactic paper and the author defined the initial state ket as |\Phi_{in}> = {\int}dq\phi_{in}(q)|q> where q is a coordinate and \phi_{in}(q) = <q|\Phi_{in}> = exp\left[\frac{-q^{2}}{4\Delta^{2}}\right] I don't know if I'm missing something but isn't this definition a...
49. ### How do you build a wave packet and inital conditions

Hi, I'm trying to get my head around Schrödinger's equation and quantum wave theory. I'll try to shortly state how I understand it so you may see where I'm wrong and better answer the question. In classical mechanics if you solve a linear differential equation, the sum of the solutions is also...
50. ### What distinguishes plane waves from wave packets in physics?

Generally speaking, what is the difference between these two? What I mean by that is: in what kind of different processes are these produced (and used in physics)?