Recent content by sonnichs

Yes--I see. Both CLAUDE and chatGPT reduce equations into LaTEX markdown. It took me a while to recognize this since i don't know LaTEX. So we have come full circle to where Filip Larsen posted. I suppose for me using the handwriting recognition is valuable--I get LaTEX in a few seconds...

Thank you for your replies. I can see the value of LaTex--a lot of people use it now. (I was born pre-sputnik) I am still looking thru the links that were sent as well. My reply is late because I did some research on this first and am finding that AI may be what works here. I am not an AI...

I am not sure where to best put this post-possibly it belongs in general physics as well. I presently use an ancient device for writing: a pencil, to enter physics equations into a notebook. Especially with arthritis and my horrible handwriting (I got a D in grade school!), it would be nice to...

Thank you Gavran. This explains my premise. -FS

I am thinking about the simple Fourier transform: F( sin(nx) ) <--> iπ( δ(ω+n) - δ(ω-n) } I believe I can represent most of the functions in classical physics, f(x), in a Hilbert space by expressing them using their Fourier components as a basis. This leads to a spectrum which is...

Thank You Jedishrfu ! I too am a fan of 3brown1blue and have sent a message as you suggested. I got my degrees 50 years ago and I think years later Grant, unlike so many others, has gone beyond the common use of computers and made use of them to visualize math. My knowledge of math is...

Are there any good visualization tutorials, written or video, that show graphically how separation of variables works? I particularly have the time-independent Schrodinger Equation in mind. There are hundreds of demonstrations out there which essentially distill to copies of one another...

Thank you for the links. I finally read thru them-I understand some but not all of what you indicated as I am somewhat limited in the area of analysis. As you said in our post there is quite an intertwining between Functional Analysis, Linear Algebra, and Analysis. Even the names don't seem...

Thank you. I probably have a half dozen books laying about titled "Linear Algebra.....". Sadly none seem inclined to deliberate much on function spaces. Hilbert spaces of functions are of great interest in quantum mechanics. I found a good hint of what you mention in "Linear Algebra...

Thank you for your reply. So I think we can safely state that for functions, the condition of additive closure is always met due to definition. fritz

Assume s is a set such that Fs denotes the set of functions from S-->F where F is a field such as R, C or [0,1] etc. One requirement for F to be a vector space of these functions is closure- e.g. that sums of these functions are in the space: For f,g in Fs the sum f+g must be in Fs hence...

Yes. I see. My first approach would not usually involve and angle. (very Euclidean?) As I mentioned I usually like to approach things without angles, using sums/linear algebra etc. "aT b" is safer for me. The main cause of my initial question was that I was thinking of ways of...

I will check Ballentine if I can get it from the library. I have "gone through" a few texts over the years, including Messiah, Schiff, Shankar and Griffiths. Can't recall any details on complex representation of angles. Perhaps I am reading too much into this. I guess my usual approach to...

Peter Sorry about my sources--they are diffuse, buried variously on the internet. But moving on to your comments, I guess you are indicating that: <> is not equivalent (a superset) of "the dot product" since the later cannot have a complex angle. I guess that is what is confusing...

I am wondering about the formal definitions of the dot-product and dirac brackets <>. Of course <> brackets apply equally to functions as well as vectors (in Hilbert space). Is it safe to assume that . and <> are equivalent? Can one state that <a|b> equivalent to |a| |b| cosT where a and b...