getafix

particularly can i use to solve for a parameter that gives me a particular eigenvalue for an eigenvalue problem..

Would someone be willing to answer a few questions about ParametricNDSolve in mathematica..

is there a more seamless way to do it?

and then data = Import["np.csv"]

on the python side

ok..I was able to patch together something.

also, say I have a numpy array in python, I want to import that as a matrix into Mathematica..is their an easy way to do it using external evaluate or otherwise?

Another quick question I know Mathematica supports ExternalEvaluate and since 11.something I can do this by beginning an input cell with ">" which produces an external code cell..and say I wanna do something in python..I have multiple versions of python on my mac, how do i specify which python to use?

also would you happen to know using NDEigensystem or otherwise, how do i specifically compute eigenvectors for specific eigenenergies..

@b3m2a1 Thank you! :)

i havent been able to locate it in the documentation

How do i view the defaults for some method in mathematica. Specifically, Arnoldi i want to know the maxiterations and tolerance..

@user21 Yup! Found it Thanks! :)

Thanks for all your help! :)

I think imma call it day for now, and see if I can catch a hold of user21 tomorrow, and if he is free, pick his brain a little..

although I just tried NIntegrate for the first 2 eigenstates over the range I plotted them, and they seem to integrate to 1..

yeah I get what you mean.

Ahh okay, I didn't know that about NDEigensystem..but then again, it has no reason to expect that in general, I supposed.

also, the Interpolating functions that mathematica spits out, after assing them to something like y[x]:=.. I can just call them and treat them like regular functions while plotting, NIntergrating etc.?

i might try picking up the cell measure on a bigger computer

^I just converted the reduced mass i had in g from my problem to atomic units (hopefully correctly)

m2 = 1.16*10^-23*10^-3*1.097768382881*10^30

L2 = -1^2/(2*m2)*y''[x] + V2[x]*y[x];

my L2 is

at least qualitatively gives me a first eigenstate that hits zero at the right boundary, and decays on the left

@b3m2a1 so..I have been dicking around with it for a bit..

I ran in the neighbourhood of the two walls, 35 and 208.and had to reduce the cell measure because it was taking way too long on my computer..do you know of a way to enforce the other BC

plotting the interpolating function from the o/p it sorta goes to zero where it is supposed on the right...but not on the left..

as far as i know for each value of M which runs from -1,0,1 the tensor operator should be proportional to a component of the vector cross product for the the case of K = 1, M = -1, I get that it is a linear combination of 2 components of the vector cross product, I am pretty sure this incorrect, unless someone here knows otherwise perhaps?

I am using the fact that the clebsch-gordan coefficients in the sum are zero whenever p+q =/= M

but, for $$[V^{(1)}\otimes W^{(1)}]^{(1)}_{-1} = (1/ \sqrt{2})V^{(1)}_{0} W^{(1)}_{-1} - (1/ \sqrt{2})V^{(1)}_{-1} W^{(1)}_{0} $$ i get terms that don't cancel out

I was able to show, $$[V^{(1)}\otimes W^{(1)}]^{(1)}_{0} = (i/\sqrt{2})(V \times W).\hat{z}$$

Things are defined as follows

a quick question, I am trying to prove that tensor operators $$[V^{(1)}\otimes W^{(1)}]^{(1)}_{M}$$ are proportional to the three components of the vector cross product of V,W

i guess it is okay just to treat it as some external field..like we would in an ising model?

I have been given no information about the origin of this field or its physical significance by my lecturer..

so, I have been given a lattice gas with $$E_\nu = \frac{-\sigma}{N}\sum_{i,j}^{N}s_is_j$$ the coupling is weak but long range not nearest neighbour and asked to compute a canonical partition function in terms of a ghost field $\phi$ which has a gaussian distribution: $$p(\phi) \propto \exp(-N \phi^2/2kT \sigma) $$ what I don't get is what does it mean to use a "ghost field" in this case

yeah i am trying to look at transitions between a|x| and infinite box, with a slanted wall, ...and well in the large L limit (length of the box)..it is just a very shallow linear potential..I can sorta get the solutions to work out, but trying to write reasonable explanations and give me self some solid intuition is hard

I can't seem to get good intuition for it, and i can't seem to find a good enough source that discusses the subtleties in detail..

yeah..

@Semiclassical gotcha. so if it is just a linear potential in space, and no boundaries..it is indeed a continuum of energies isn't it?

clearly there is a gap in my understanding somewhere

I had a quick question about quantum mechanics, for a particle in a linear potential say -c*x, the energy eigen spectrum should be continuous? but we solve the time independent schrodinger equation by transforming it into a airy equation and then the roots of the airy function correspond to energies. I guess this is at odds with my intuition for the energy spectrum to be continous? but then the we normalise the airfunctions to a delta-function like we would for continous case...?