Illusion that shell, subshell and orbitals are the same

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High school education often simplifies complex concepts in chemistry, leading to the misconception that shells, subshells, and orbitals are identical. Teachers typically avoid advanced mathematical explanations to accommodate students' foundational knowledge. The distinction between these terms becomes clearer with a deeper understanding of quantum mechanics and atomic structure. Resources like the Schrödinger equation provide a more accurate representation of atomic behavior, especially in multi-electron atoms. This simplification is intended to ease the learning process but can result in misunderstandings later on.
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Why was I taught in high school that shell, subshells and orbitals were the same thing?
 
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avito009 said:
Why was I taught in high school that shell, subshells and orbitals were the same thing?

Because your high school teachers (almost certainly rightly) didn't think that you had the mathematical foundations needed to handle something like http://users.aber.ac.uk/ruw/teach/237/hatom.php (Picked pretty much at random, one of many thousands of explanations that you will find if you google for "Schrodinger hydrogen atom solution"), let alone the additional complications that arise in multi-electron atoms.
 
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Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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