Recent content by zenterix

Right, so this is what effectively prohibits the solution ##\psi(x)=0##.

Here is why I think I am asking this. We had a 2nd-order linear ODE. The characteristic equation was $$p(s)=s^2+k^2=0$$ with discriminant $$\Delta=-4k^2$$ and with roots $$s=\pm ik$$ But if ##n=0## and so ##k=0## then the discriminant is zero and we have only the single root ##s=0##...

I have a question about one of the steps in the calculations. For context about where in the calculations I am, we assume that a particle is subjected to a potential energy function that is infinite everywhere along the ##x##-axis except for a line segment of length ##l## where the potential...

Okay, but why are there the two theorems? What makes them so different?

Okay, let me try to go through why there are the two theorems in steps here. Ok, so ##A## is definitely ##n\times n##. Is ##F## ##n\times 1##? Right after the above, there is a proof that for any ##n\times n## matrix ##A## and any scalar ##t## we have ##e^{tA}e^{-tA}=I##, proving that...

I never really understood why there are these two separate theorems in the book.

I mean, maybe there isn't a typo. If ##B## is ##n\times n## then don't we have ##n## initial value problems? ##F(t)## is said to be ##n\times n##. Is not each column of ##F## a solution to one of the ##n## IVPs? Just a little later in the book there is the following theorem Now, ##B## is...

Consider the differential equation $$y''+ay'+by=0$$ We have analytical solutions for this equation. There are three cases to consider based on the discriminant of the characteristic polynomial associated with the equation. $$\Delta=a^2-4b$$ I just want to discuss the case where $$\Delta...

This is a problem from this problem set from MIT OCW., Here is my reasoning about the problem, even though I don't reach any conclusion since I am not sure what is being asked. The decay rate of the number of nuclei of technetium in our sample is $$\frac{dN}{dt}=-k_rN=\text{activity}=A$$...

This is the final problem in this problem set from MIT OCW. Here is what I did to try to solve it The table cited in the problem is below We can easily spot the two redox couples that are in the electrochemical cell we are given. The hydrogen-based electrode has standard potential zero, and...

This problem is from this problem set from MIT OCW. Here is how I tried to solve the problem. Looking at the table above, we see that the top-to-bottom order is from largest to smallest standard cell potential. Since gold, ie Au, is at the top, every other redox couple on the list has the...

I've never heard of Faraday's law of electrolysis. So, where does the electric field generating the current come from? In other words, where does the emf come from? In a simple electrochemical cell, we have a closed circuit formed by a wire connecting the electrodes and a salt bridge...

From the molar mass of tungsten of 183.84 g/mol, we know that ##100/183.84\approx 0.55## mol was deposited. We also know how many mols of electrons passed through the solution in an hour. This comes out to about 1.12 mol of electrons. So, at a very superficial level of understanding, I...

Here is my guess. Not all electrode reactions include a conducting solid as a reactant or product. A hydrogen electrode, for example, includes hydrogen gas and aqueous hydrogen cations. There is, however, a chemically inert metallic conductor present, such as an unreactive metal or graphite...