Recent content by paradoxymoron

First, I have a question regarding the conservation of probability. The book shows (quite elegantly) that $$ \frac {d}{dt} \int_{-\infty}^{\infty} |\Psi (x, t)|^2dx = \frac {i\hbar}{2m} \Big{(}\Psi ^* \frac{\partial \Psi}{\partial x} - \frac{\partial \Psi ^*}{\partial x} \Big{)} \Big...

When you say the induced EMF sources energy, do you mean it's adding energy to the system? I find that pretty neat, since I've only encountered energy-eating non-conservative forces so far (I haven't taken E&M yet). In your example of the time-varying voltage, is there a force responsible for...

In my intro to Quantum Mechanics course, my professor gave a little aside while exploring the analogy between the Schrodinger Equation and Newton's second law: in classical physics, energy is conserved when the potential energy is not a function of time. I wanted to try to answer this my self...

By "making sense," I believe you are asking for an intuitive understanding of the vector operations. I asked myself this same question last year, since I try to make sense of all math lore I learn, and I believe this site does a marvelous job of explaining them. Also note, this is not probably...

I don't see anything wrong with your work.

The course load so far has been somewhat heavy, but I managed to do well. I actually do want to do a graduate degree; it's all about the learning experience for me. Academia does attract me more than any other area. I guess I can use the extra time I'll have double majoring to think about what I...

I actually enjoy having my electives being math-oriented. I have already explored different areas while I was taking gen-ed courses. Philosophy/Ethics was the only thing that interested me. And I guess you're right about the double major qualifying me for either graduate school. I'm still not...

In physics with calc (1 and 2), I only remember using separation of variables, but I did not take either course at UF. Gauss Law was heavily reliant on some knowledge of integration, however. I believe ODE should be taken after calc 3, but after calc 2 is okay, too. ODE was used more in...

I took Modern Physics at the University of Florida this Spring 2015 semester. ODE's did not play a major role in the course, but was useful in understanding the derivations of situations involving the Schrodinger Equation. I earned an A in the course and the professor was superb. I hope you join...

Hello, PF! Some background information on me: I am currently a third-year physics undergraduate and I am in the process of choosing my classes for the upcoming semester. I have to take some math electives, which lead me to rekindle the thought of double majoring alongside math. Math and physics...

I think I have a feel for it now that i know a little about its physical use. But, I regress. I suppose I'll leave it until future courses to give me a complete explanation, together with a rigorous derivation and meaning. I'm glad I wrote this topic. It showed me that there are some things that...

What I'm trying to ask is that since we found the derivative is ##\frac{dy}{dx}=\frac{1}{xy}##, we have two options for ##y## now, the positive or negative root, since we squared the term to make the differentiation simpler. Why do we necessarily choose the positive one? I know I'm just being...

Hm, how does this take into account the fact that squaring the equation will give multiple values? ##y^2=2\ln(x)+1## is a set of two equations, namely $$y= \sqrt{2\ln(x) + 1}$$ and $$y= -\sqrt{2\ln(x) + 1}$$ Will the derivative also be multiple valued? It doesn't seem like it since...

Ah, I can see how in inverse transform is "integrating away" the ##s## variable to attain the original function ##f(t)##, just as how the regular transform does the opposite. The inverse integral in that link looks pretty intuitive (with some complex constant next to it), but still no...

I'm not sure I understand this time and frequency business; perhaps I am not that far in my career to know about it. I used the Laplace Transform extensively in my ODE course and I understood its use of simplicity but not what it means or its motivation. Sure exponentials have nice...