I still have no clue where i am stepping into.
I can certainly say i do not grasp it.
I may be able to solve a question or two, but this is simply because of my knowledge of mathematical patterns. I have no intuition or whatsoever regarding what’s going on down there.
However this mathematical description of hydrogen gives us these spherical harmonics (the angular dependance of hydrogen’s wavefunction).
When i was still an AS Chemistry student i can remember seeing a figure like the one above (but in 2-D) with the explanation that in those ‘clouds’ lies the the hydrogen’s electron i.e the probability of finding it….i suppose that would still be ok if you did some extra more maths…
If you do NOT know Quantum Mechanics, please stop seeking answers to questions (too extensively).
Forget all about it.
DO NOT MEDDLE WITH QUANTUM MECHANICS. It is disturbing.
Leave the work to someone with excellent math knowledge-skill-talent/loads of free time/determination.
For people who cannot separate their life from their work that would inevitably lead to a no life situation, as your brain would have eventually become a gel of physical constants and graphs in 3D and perhaps 4D (not to mention N-D) space.
I’d rather go out and have a tiropitta.
But then on the other hand…the father of all this quantum math representation, Schroedinger, was certainly not a geek. He was a serious NON-monogamist. It is a well known fact that he discovered his (Schroedinger) equation whilst having holly-days with his girlfriend (not his wife) upon some mountains in Austria (having intimate moments)…
So there you go.
The time-dependent one-dimensional Schrödinger equation is given by
Schroedinger Eqn in Spherical Polar Coordinates
If the potential of the physical system to be examined is spherically symmetric, then the Schrodinger equation in spherical polar coordinates can be used to advantage.
For a three-dimensional problem, the Laplacian in spherical polar coordinates is used to express the Schrodinger equation in the condensed form
Expanded, it takes the form
This is the form best suited for the study of the hydrogen atom.