# Accidental degeneracy in Hydrogen Energies [duplicate]

The energy of Hydrogen electron ground state should depend on $n$ and $\ell$, but it only depends on $n$. What is the reason behind this accidental degeneracy; I know that the reason lies in symmetry; but can someone explain me in simple terms. PS: I do not have knowledge of Group Theory!

## marked as duplicate by Emilio Pisanty quantum-mechanics StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Feb 22 '18 at 16:56

• There are plenty of technical answers to the original question. The question is what transformation transforms circles into ellipses? (and it's not a "squish"). In this case its a hidden SO(4) symmetry that conserves the Laplace-Runge-Lenz vector. The Lagrangian is invariant under these hyper-rotations (which are w.r.t to the orbital plane and in 4th spatial dimension), with the projection of the orbit into $E3$ being ellipses of varying eccentricity (and hence different total angular momentum). Not easy to visualize. – JEB Feb 22 '18 at 18:15