Recent content by ja07019

Thank you for the response. I have been trying to figure this out but I can't seem to get the answer the book gets. Here is my work for the Probability Current In region 3, ##J_3 \propto \psi_3^{*} \frac{d \psi}{dz}-\psi_3 \frac{d \psi_3^{*}}{dz}## ## =...

Sorry about that. I have made those edits.

There are 3 regions, to which I split the function as follows. I can derive the solutions myself. However I need to verify whether I am using them properly. There are two principles/ideas that I am not sure if I am misinterpreting. 1) Anytime a wave is incident on a discontinuity(such as when a...

The probability density function so I can find <value>

Thank you for this. Classically the system will have two values, but there magnitudes are equal. The only thing I am now concerned about is lacking some kind of pdf to bring about the variances for momentum and position in a way that both values are found using the same pdf But I have to say...

Some posters on SE have suggested that the issue lies in the boundaries if that helps.

I apologize to all of you. I too am not sure what the book is using as a marker for classical particles. As I understand, wave particle duality is still classical mechanics while probability density waves are QM. So it is likely I am wrong here(but that should have nothing to do here). Anyways...

Well no I am just trying to prove a weak version of the corresponds principle. If you notice something, the wavefunction in QM contains n(energy level) but the classical does not. So there is really no way to let n go to infinity as neither sine nor cosine have some definite value here. However...

I think I should be a little bit more clear, I have found the quantum mechanical solution per Probability theory, but now I am trying to arrive to the correspondence principle via another route, the classical route. I can see how I can reach the same conclusion by applying such limits to the...

The problem explicitly says that this is a classical particle(ie no Probability involved) but everything else should work the same.

Sorry. It's not a ball it's a particle(which also behave as a wave). It's not a quantum particle in that there is no probability involved

I might be doing this wrong. But the point I would like to get across is once again that the magnitude of the wavefunction is given by |u(x,t)|, where u is the wavefunction. Now if the wavefunction is a real sinusoid, then the wavefunction's derivative(the velocity) will be sinusoidal. This...

All of what you said is definitely correct. At this point I am not so sure if I am using the correct Probability Density Function. However, what I would like to point out is that the problem outright says that the particle bounces around with a uniform velocity. The only way to have uniform...

Classical in the sense that there is no probability involved, more precisely the problem simply says to attempt to treat the wave function of a classical particle(deterministic states) as a stochastic state. Naturally, it makes no sense to treat the propagation of a deterministic wave as a...

Okay I can see why this is necessary for QM(solving Schrödinger's Eq). How would I go about setting up the boundary conditions here? Do I just split the solution into a sine and cosine wave and use the asymmetrical vs symmetrical? The problem I have with that is that the wavefunction is no...