I'm new to this but I'm assuming you're referring to the time-independent non-relativistic equation. Let \psi(x_0) represent a potential value where kinetic is 0. Let \psi'(x_0) represent kinetic value where potential is 0. Iff \psi(x_0) and \psi'(x_0) are two separable wave functions that...
I will only speak for myself: If I call a subject hard, it makes it that much harder for me to get through it. If I allow my passion/interest to guide me I will pursue a certain subject for as long as my passion/enthusiasm dictates. Ever heard the cliche: You can do anything you put your mind...
I have never thought the sun was yellow. It is too bright for me to observe for more than 5 seconds (even with very dark sunglasses). Color doesn't seem to be an objective measure since I cannot tell if my perspective of a certain color (in this case, yellow) has the same shade/physical...
The aim of my research is to show that some set (#) axiomatically perceived as deviating from the non-'0' entity will subscribe to a non-'0' collection (#) of perspectives (interpretations) on said finite characters from the finite interpretations (predicated on only 1 of 5 senses a.k.a. vision...
I'm pursuing a computational neuroscience degree. My personal advice would be to thoroughly investigate the research techniques/principles of your area or specialty and take courses as well as additional classes from websites such as coursera.ra and MIT Opencourseware vids on YouTube (typically...
I am a 22 year-old male in the U.S. My fascination (or obsession) for math/computational neuroscience/set-theory/Analysis & Topology topics has reached nearly unprecedented levels in my life to the point of posing a detriment to my personal life (insomnia, pickiness, and periodic rage). I never...
I guess I'm looking at this trivially, and no offense to anyone, but the fact that there is even a paper that seeks to compare the degree of relevance between the social and physical sciences suggests that these 'social scientists' (implying the authors of this paper, not all the people in the...
This book is so atrociously bad I don't even know where to begin. No offense to people who appreciate this text but the equations are practically smashed in your face. I am looking at the rotation/angular momentum chapter (10) of the 7th ed. and there is absolutely no proof-development for...
Any time. You asked "when is it ok to do this", and I assumed that it was always ok to do that since both terms can be rewritten and equate to each other by definition. I'm not sure if if I'm oversimplifying the question, but unless there is a bound-problem with g_x this seems to be more a...
This is a trivial way of showing that what you have written is valid, but I'm guessing you already know it. I'm assuming \delta is dirac, so for \delta ≠ 0:
Since g_x \rightarrow \frac {\partial g}{\partial x}, \delta \cdot g_x = \delta(\frac {\partial g}{\partial x}) and \frac {\partial...
I apologize for posting in a rush.
L is a maximal flag defined by L_0 \subset L_1 \subset L_2 ... and L_i is a space for which ({e_1, ... ,e_i}) forms the basis. Assuming
({e_i, ... ,e_{i-1}}) is valid, M is a linear span of the aforementioned basis of L_i.
My goal: To show the dimension of space L equals the length of any maximal flag of L;
Is the following valid?
My attempt:
Let M \rightarrow {L_{i-1}, ... L_i}
where {e_i} \in L_i | e_i \not\in L_{i-1}
Assuming e_i \in M and e_i \not\in L_{i-1},
we can say: e_i \in L_i and L_i...