Recent content by JeremyEbert

I guess my question comes down to; Can I visualize the ladder operator values as vector rejection values? http://en.wikipedia.org/wiki/Vector_projection#Vector_rejection_3

Ah, I've heard them described as "in between the state vectors", this makes sense. Is the intensity of the transition between the states referring to the intensity of the magnetic moment? Does this have something to do with the Larmor frequency? Thanks again for your responses.

Thanks dextercioby. Being very new to the concepts of Hermitian operators, I am obviously having a hard time grasping this explanation but I will continue to research the subject. My question stems from something I read on OEIS related to NMR spectroscopy. Stanislav Sykora, among other...

What is the significance of the ladder operators eigenvalues as they act on the different magnetic quantum numbers, ml and ms to raise or lower their values? How do their eigenvalues relate to the actual magnetic transitions from one state to the next?

A pronic + 1 is a centered polygonal number. ∏(1/2 + √n) gives no information about ∏ itseft, it is trivial.

Ah yes, the floor function is a bit redundant. Thanks for that. This obviously relates then to the square root of a oblong (pronic) number + 1/4 having a half-integer value. The name "oblong" indicating they are analogous to polygonal numbers.

Norwegian, Sorry for the extreme lack of precision. I definitely forgot to include a key part while typing this up. Obviously, ∏(√n) increments exactly when n=p2. However ∏( Floor(√n + 0.5) ) increments only when n is a centered polygonal number with a prime index. It seems like a proof of...

Is there a proof that ∏(√n) increments only when n is a centered polygonal number with a prime index? ∏(n) is the prime counting function n=p^2-p+1 for a prime p 3, 7, 21, 43, 111, 157, 273, 343, 507, 813, 931, 1333... http://oeis.org/A119959

Bill, Here is a 3D model of possible S_x and S_y states based upon the ladder operators. You will need the Flash plugin to view. This runs through all Spin states up to s=75/2. http://dl.dropbox.com/u/13155084/SPIN/index.html

Bill, If you think of the possible spin states as a function of the magnitude of spin then: |S| = magitude S+-=|x +- iy| = magnitude applying the ladder opperators on the S_x states one could come up with something like this model. Notice the X-axis...

Bill, Thank you again. I assumed the values of Sx and Sy would be quantized as well. It seems logical seeing as the Z axis is actually an arbitrary direction usually determined by an external magnetic field. Sz is just used for convention, we could substitute Sx and Sy just as easily. Is there...

Thanks Bill for you insight. I am very new to this vector/spinor model, hence my unusual view. I have heard that there is some controversy about all these quantum and non-quantum visualizations of spin from Stan Sykora. He maintains the high-resolution NMR spectra simulation dll in Mnova...

I can't seem to reconcile a part of the vector model of spin and some of its operators. to quote wiki just above the "Bohr model" section: http://en.wikipedia.org/wiki/Vector_model_of_the_atom#Mathematical_background_of_angular_momenta "2.The magnitude of the vectors must be...

unchained1978, On page 7 this paper shows geometry associated with the spin operators. http://www.columbia.edu/itc/chemistry/photochem/spin/03.pdf http://www.easyspin.org/documentation/spinoperators.html I can't figure out how the Sx and Sy fit in this vector model. I must be...

This is a VERY good paper. http://www.ejournal.unam.mx/rmf/no546/RMF005400609.pdf