This is a section about Atomic orbital!
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This is a section about Principal quantum number!
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This is a section about Azimuthal quantum number!
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This is a section about Magnetic quantum number!
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This is a section about Atomic orbital!
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In the case of the Schrödinger equation solution for the hydrogen atom, each orbital is one eigenvector of the solution.
Remember from time-independent Schrödinger equation that the final solution is just the weighted sum of the eigenvector decomposition of the initial state, analogously to solving partial differential equations with the Fourier series.
This is the table that you should have in mind to visualize them: en.wikipedia.org/w/index.php?title=Atomic_orbital&oldid=1022865014#Orbitals_table
An atomic orbital is a mathematical function that describes the wave-like behavior of an electron in an atom. This concept arises from quantum mechanics and is fundamental to understanding the structure of atoms and the arrangement of electrons within them. Here are some key points about atomic orbitals: 1. **Shape and Energy**: Atomic orbitals have distinct shapes (spherical, dumbbell-shaped, etc.) and energy levels. The shape and orientation of an orbital are determined by the quantum numbers that describe it.