Recent content by Saraphim

I think I understood what I was missing. I needed to set all terms in the product with exponents higher or equal to 4 to zero. Approximation is not my string suite. Thanks for the help!

But how is that so? In the unexpanded P without substituting in \epsilon = 2b/a, I have e^{-2b/a}.

Thanks for your response! I have a few problems, still. First, I feel the Taylor expansion should be 1 - \epsilon + \epsilon^2/2 - \epsilon^3/6 +\ .... Isn't that right? Second, I feel that I should be able to realize that the terms lower than the cubic somehow get canceled out, but I really...

Homework Statement What is the probability that an electron in the ground state of hydrogen will be found inside the nucleus? a) First calculate the exact answer, assuming the wave function \psi(r,\theta,\phi) = \frac{1}{\sqrt{\pi a^3}} e^{-r/a} is correct all the way down to r=0. Let b be the...

Solution: The expression for \psi_n is already normalized. I should have realized this. Therefore, the integral yields 2 over the interval

Homework Statement A particle in the infinite square well has its initial wave function an even mixture of the first two stationary states: \Psi(x,0) = A\left[ \psi_1(x) + \psi_2(x) \right] Normalize \Psi(x,0). Exploit the orthonormality of \psi_1 and \psi_2 Homework Equations \psi_n(x) =...

It is not a linear model (even though it is a linear differential equation) - if you plug in x(t)=10*exp(-t/50) into the equation for x'(t) this will be quite clear, and your results are, as far as I can see, correct. Regarding b) I have no idea. Try posting a new question with that specifically.

Let x'(t) be the rate of change of salt in the tank and x(t) the amount of salt. Then: x'(t) = -2 L/minute * x(t)/(100 L) since x(t)/(100 L) is the concentration at any given time.

Try describing the rate of change as an equation involving x(t), the amount of salt at any given time in minutes. Once you've done this, you should have a linear differential equation. Do you know how to solve this?

Wow, okay, that was utter nonsense. I've now managed to confuse myself to the point where I don't know what I'm doing.

To elaborate a bit, what is stumping me is that both functions completely discard any information about z, and if I take, for instance, \tilde{f}_x((x,y,z),t) for any set values of (x,y), then the result doesn't depend at all of z! This would make the wave propagate as a cylinder with infinite...

Homework Statement Two speakers at (x,y,z)=-L,0,0 and (x,y,z)=(0,-L,0) Find the amplitude at all positions in the plane x=y Homework Equations The waves are given by: \tilde{f}_x(\overline{r},t)=\frac{A}{r_x} e^{i(kr_x-\omega t)} \tilde{f}_y(\overline{r},t)=\frac{A}{r_y}...

I can't seem to find out which two meshes are independent. :rolleyes:

Wait, no, that's wrong. I'll think on it some more.

So the first independent mesh is the one containing R1 and R3 and the other containing R3 and R2?