What is the difference between the Bohr model of the atom and The solution of the Schrödinger equation for the hydrogen atom?

Are there any difference between definition of the electric potential energy (of a hydrogen atom) In the Bohr model of the hydrogen atom and The solution of the Schrödinger equation for the hydrogen atom?

The potential energy is simply that of a pair of point charges:

$$U_{(r)}=-\frac{e^2}{4\pi\epsilon_0 r}$$

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    $\begingroup$ The basic difference is that the Bohr model tells us that electrons have fixed paths while the Schrodinger equation incorporates the Uncertainty principle. So, unlike the Bohr model, it tells us about the region where the electrons are likely to be found. $\endgroup$
    – Yashbhatt
    Sep 24, 2014 at 10:02
  • $\begingroup$ Can you be more precise about what you're asking? The Bohr and Schrodinger models are conceptually completely different so any comparison is a bit absurd. Were you maybe wondering what the Schrodinger model correctly describes that the Bohr model does not? $\endgroup$ Sep 24, 2014 at 10:59
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    $\begingroup$ Bohr model is ad hoc -type one trick pony for explaining energy levels of hydrogen atom. Two dimensional toy model cannot represent the real world. Bohr's theory is not quantum mechanical but Schrödinger's theory is. $\endgroup$
    – user59412
    Sep 24, 2014 at 11:52
  • $\begingroup$ @John Rennie Is definition of the electric potential energy of a hydrogen atom same thing for both models? $\endgroup$
    – Achmed
    Sep 24, 2014 at 11:59

2 Answers 2


The potential energy function is the same for both.

The energy level solutions are the same for both.

The key difference is that in (most modern interpretations of) the Schrodinger model the electron of a one-electron atom, rather than traveling in fixed orbits about the nucleus, has a probablity distribution permitting the electron to be at almost all locations in space, some being much more likely than others (or according the Schrodinger's original thinking, the electron is actually smeared out over space, rather than being at a point).

  • $\begingroup$ Is this true for all spherical potentials or only for electromagnetism? $\endgroup$
    – arivero
    Sep 25, 2015 at 13:15

In addition to what @DavePhD says, the Schrodinger model also calculates the angular momentum correctly and shows the angular momentum degeneracy of energy states.

A similarity between the results is that the Bohr model orbital radii are equal to the mean radius, $<\psi|r|\psi>$, values of some of the angular momentum states.

  • $\begingroup$ The Schrodinger equation doesn't give a mean radius or radius expectation value that is the same as the Bohr model radius. For example, in the hydrogen ground state, the mean radius is 1.5 times the Bohr radius, but the most probable radius is the same as the Bohr radius. hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydr.html $\endgroup$
    – DavePhD
    Dec 18, 2015 at 12:14
  • $\begingroup$ My bad, @DavePhD. Most probable, not <r>, is right. $\endgroup$
    – Bill N
    Dec 19, 2015 at 4:04

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