Wave packet Definition and 111 Threads

Hi, I've got the right answer in this problem, but I'm not sure if I've got the correct reasoning Homework Statement A Gaussian wave packet travels through free space. Which of the following statements about the packet are correct for all such wave packets? I. The average momentum...

For a free particle,the one dimensional Schrodinger's equation gives a solution of the form Ae^i(kx - wt).This solution does not meet the normalisation requirement.According to Bransden-Joachain's texr,there are 2 ways out of this difficulty.One is to superpose and form localised wave...

I’m currently taking a class in fluids in which we are studying different types of wave propagation. We discussed how for certain types of waves (such as deep-water ocean waves), the frequency (and phase speed) of each sinusoidal component is a functions of the wave number. This makes the...

I am working on a problem that goes "Show that for a wave packet propagating in one dimension, for a free particle Hamiltonian" m d<x^2>/dt = <xp> + <px> What I think I want to do. Use d<A>/dt = i/hbar * <[H,A]> Which leads me to d<x^2>/dt = i/hbar * <[H,x^2]> For the free...

"The particle and the wave picture are both simplified forms of the wave packet description, a localized wave consisting of a combination of plane waves with different wavelength." it's confusing. Can somebody explain it? particle is an object, it seems wave is also an object.How to combine...

Consider a wave packet represented by \Psi (x,t) = \int_{k-\Delta k}^{k+\Delta k} A \cos\left[k'(x-ct)\right] dk' A constant and ck' is the dispersion relation SOlve th integral and describe teh propogation properties of this wave packet. Assume this means that the phase and group...

Hi, I'm trying to figure out what the group and phase velocities of a wave packet describing a particle are in the relativistic case. I started with the relationship between energy and impulse : E squared = p squared X c squared + rest mass squared X c to the fourth. In this, I input the...

In my wave final there was a quetion that went "Write the most general expression for a wave paquet in terms of a Fourier integral and explain what this integral corresponds to physically." What would have you answered to the second part of the question?

The similarities between the classical wave packet and the QM photon are striking. They both move at the group velocity. They both are subjected to an uncertainty principle. A classical wave packet is like a photon a region of concentrated energy, ... So is a photon something like the...

I was wondering if anyone can give me some assistance on a homework problem. Here it is, Consider a wave packet defined by \begin{equation} \vec{A}(\vec{r},t)=\int \hat{\mathcal{A}}(\vec{k}-\vec{k_0}) \frac{e^{i(\vec{k}\cdot\vec{r}-\omega(k)t)}}{(2\pi)^{3/2}}d\vec{k} \end{equation}...

I read that a wave packet is really some superposition of some waves with different wave number k (just slightly different k's). While the wave packet represents the particle, is there any meaning to the individual wave? How does physicists know what to superpose?