Quantum Mechanics Answers

the spin matrices for s=1 are given show that their squares sx^2,sy^2,sz^2 are commutative construct thir eigen vectors what geomatrical significant do those vector posses?

Is photon emission possible without electrons changing energy levels?
Does molecular vibrational transition and consequent emission of infrared radiation involve electrons changing energy level? In wikipedia, about vibronic transitions it says "Most processes leading to the absorption and emission of visible light, are due to vibronic transitions. This may be contrasted to pure electronic transitions which occur in atoms and lead to sharp monochromatic lines (e.g. in a sodium vapor lamp) or pure vibrational transitions which only absorb or emit infrared light.". Does this mean infrared radiation is emitted without electrons playing a direct part? What about changing in molecular rotational energies? Also, I understand reflection is not a radiation absorption-emission phenomena, so can you explain what actually happens to the photons? Same thing for radiation scattering.

Find the probability distributions of the orbital angular momentum
variables L2 and Lz for the following orbital state functions:
(a) Ψ(x) = f(r) sinθ cos φ,
(b) Ψ(x) = f(r)(cos θ)^2,
(c) Ψ(x) = f(r) sinθ cos θ sin φ.
Here r, θ, φ are the usual spherical coordinates, and f(r) is an arbitrary
radial function (not necessarily the same in each case) into which the
normalization constant has been absorbed.

i want to plot the potential energy curve based on data i've produced. I have the energies, distances and a 6 parameter data. how do i get a model function to base my plot on. how do i curve fit my plot

Find wave functions of the states of a particle in a harmonic oscillator potential
that are eigenstates of Lz operator with eigenvalues -1 h , 0, 1 h and have smallest possible eigenenergies. Check whether these states are also the eigenstates of L^2 operator. Eventually, write the wave functions using spherical coordinates and normalize independently
their radial and angular parts.

Does any device that can perceive and record data constitute an observer? If a non-human sensor or recording device "observes" a quantum event, does the stored information exist as a wave of possibilities until it is examined by a human one?

I am new to quantum physics and I am just looking for information on how to get some materials for experiments as a hobby. I am looking to just dive into some areas (Basic quantum mechanics for a base and then specifically quantum levitation) and see where it takes me. This is all just for fun for me but the problem Is I dont know where to get started or how to get any useful materials. If you could point me in the right direction or tell me who I can try to contact to get this information I would really appreciate it. Thanks.