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New theories must in some approximation must reduce to older approximately correct theories. In what approximation exactly does the angular momentum quantization condition from Schroedinger's equation reduce to that of Bohr?

According to wave mechanics, $$L=\sqrt{\langle\hat{L}^2\rangle}=\sqrt{\ell(\ell+1)}\hbar$$ According to Bohr model,$$L=n\hbar.$$

I tried equating the two and expected that Bohr model will give one of the subshells, but got impossible relations between $n$ and $\ell$. In what mathematical approximation will the two $L$s coincide?

Qmechanic
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Manas Dogra
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    For large $l$ these are both evenly spaced in units of $\hbar$ but honestly the Bohr model is just wrong, especially when it comes to accounting for angular momentum since the real ground state has $l=0$ which Bohr thinks is impossible. – jacob1729 Sep 03 '20 at 15:31
  • Possible duplicate: https://physics.stackexchange.com/q/288634/2451 – Qmechanic Sep 03 '20 at 15:42

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