How the wave equation relates to Newton's Second Law of Motion

Rich667
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Homework Statement


Open Question 3.bmp

Homework Equations




The Attempt at a Solution



Open Answer 3.bmp

Any help with this would be greatly appreciated
 

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consider a small sting segment with (different) tension force vectors acting on each end, and write down Newtons second law in two orthogonal directions
 
I think the problem lies in the definition of F and acceleration a. In answer 3.bmp the F is defined as the tension in the rope, which is coaxial to the string, while the second derivative of y , the acceleration of an element with coordinate (x,y), is vertical to the string. Surely you can't say F=ma with F and a pointing to 2 different directions.
 
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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