Here is a thread. I was somewhat surprised to see the unemployment rate of physics people higher than other majors I might have naively thought would be less employable. I didn't really dig in to see if there was some harmless reason for the higher rate (for example, it might take a physics...
That's what I got. And then you would need to solve for the time from ##r(t_f)=R##. With that time you could integrate the relationship ##r^2\dot{\phi}=R v_o\sin(\theta)## to get the difference in azimuthal angle from the starting position to the final position. Multiplying that angle by ##R##...
That's the kind of mess I'm getting as well now that I worked through it more carefully. Even with the simplification on the functional form for gravity, I don't think there will be a nice closed form solution for the range.
I think with your simplification of a constant radial force and a good choice of coordinates, the answer follows fairly straightforwardly. I get ##d=\frac{2 v_0^2 \cos(\theta) \sin(\theta)}{g}##.
EDIT: Of course, I could have made all kinds of errors, so my answer may be meaningless without the...
There should be a reason for fitting something to curve (unless you just want a pretty smooth line, then just use interpolation). For example, when parameters in the fitting function correspond to physically meaningful parameters. Do you know of any theoretical calculations of the quantity you...
I think your question fits under Sturm-Liouville theory. From a mathematical point of view, problems on a compact domain are much simpler than cases where some aspect of the domain extends to infinity.
Alternatively, stated in algebraic terms, you'd want to look at spectral theorems .
I think it would be fair to say that whatever change you made, you moved one of the eigenvalues to zero (or near enough to upset a computer numerically calculating the inverse).
Studying physics is not a job training program. Anyone studying physics should appreciate that they are going to have do the leg work to develop skills (or know how to translate their skills for a job interview) valuable to whatever job/industry they will seek out. In almost all cases, when you...
Using "information" to explain things in physics has always been anti-illuminating to me. Generally, information can be formulated a number of different ways. When we're doing physics, we can just say what we mean without the added baggage of information. Fortunately, the arxiv paper shared in...
Have you talked to the HEP theorist you work under about this? They know more about you than we do and they probably know more about the specific areas you want to work in. I'd also caution you against conflating coarse-grained prestige of institutions with the actual strength of research programs.