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Why do orbitals of hydrogen atom have same energy? If we take $p$ and $s$ orbitals, they are located at slightly different distances from the nucleus. So ideally there must be an energy difference. Moreover, if energy is same, why have two distinct orbitals? P.s I am a highschool sophomore. Pleases use simple terms.

Nachiketas
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    Look at the wonderfully beautiful answer in: Why are the higher angular momentum states of a hydrogen atom closer to the nucleus? – naturallyInconsistent Jun 26 '23 at 10:21
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    @naturallyInconsistent Nothing in that answer notes that degeneracy mean symmetry, and the degeneracy in $l$ (or in the eccentricity of an orbit in the classical domain) is due to a hidden $SO(4)$ symmetry in a $1/r^2$ potential, about which much has been written. – JEB Jun 26 '23 at 14:25
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    @JEB It is very easy to find answers on the site about the symmetry degeneracy that you are talking about, but one that talks about the wavefunction bunching up to maintain the same mean distance from the nucleus is so rare that I think it totally deserves an amplification. The answer linked directly answers the OP, that the apparent change in the look of the radial wavefunction happens to still have the exact same physically relevant mean distance. The different look is thus only an illusion. – naturallyInconsistent Jun 26 '23 at 14:32

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