The ground state of the infinite square wel

ttiger654
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Is the ground state of the infinite square well an eigenfunction of momentum?? If so, why. If not, why not??
 
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You should take these kinds of questions to the homework section of the forum.
 
Write down the ground state in x representation and try the momentum operator on it. Do you get back a multiple of the ground state?
 
I think that Dick has adequately covered the mathematical aspect of it. Now let's think about some common sense physics. Imagine a classical ball bouncing elastically between two rigid walls (let's neglect gravity here). So kinetic energy is conserved at each collision, right? But the momentum is obviously not conserved, as the ball spends half its time going left and the other half going right. (Recall that momentum has direction).

Caveat: Normally, thinking of quantum particles as classical particles is ill advised, but this is one of those situations in which the classical result carries over to the quantum scale.
 
Thread 'Need help understanding this figure on energy levels'

Thread 'Need help understanding this figure on energy levels'

This figure is from "Introduction to Quantum Mechanics" by Griffiths (3rd edition). It is available to download. It is from page 142. I am hoping the usual people on this site will give me a hand understanding what is going on in the figure. After the equation (4.50) it says "It is customary to introduce the principal quantum number, ##n##, which simply orders the allowed energies, starting with 1 for the ground state. (see the figure)" I still don't understand the figure :( Here is...
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Thread 'Understanding how to "tack on" the time wiggle factor'

Thread 'Understanding how to "tack on" the time wiggle factor'

The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
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