Standing Waves in Bohr's Circular Orbit: Interference Explained

[roshan2004]

If electron waves weren't standing waves in Bohr's circular orbit, why and how would the waves interfere ?

 

[vanhees71]

Here, several models are confused. Bohrs model has nothing to do with waves at all. It's an ad-hoc assumption built on classical mechanics, separating out the "Bohr orbits" by a quantization condition on the action of bound (quasiharmonic) motions. This model works as it is by chance for the harmonic oscillator and the non-relativistic hydrogen atom and has become completely unnecessary to deal with with the discovery of the modern quantum theory (Heisenberg-Born-Jordan 1925, Dirac 1925, Schrödinger 1926) and shouldn't be considered anymore, particularly not in introductory treatments of quantum theory, because it provides a completely wrong picture about nature in the atomic and subatomic realm.

Then there has been also some predecessor of modern quantum theory which appeared at around the same time as Bohr's model. It's become (in)famous under names like "wave-particle dualism". This goes back to de Broglie, who had the ingenious idea to describe particles as waves (as photons are described as a kind of "light particles" but on the other hand also as electromagnetic wave). Again one cannot stress clearly enough that also this idea leads to contradictions and is also a misconception on a qualitative level!

The only theory, withstanding so far any test (and there are very hard tests!) to disprove it, is modern quantum theory with the Born probability interpretation of the states, which in certain special cases of non-relativistic quantum theory can be described by "wave functions", which obey a partial differential equation with wave-like solutions. However, these wave functions are not to be confused with classical fields, because they have a probabilistic meaning, i.e., their square $|\psi(t,\vec{x})|^2$ is the probability distribution to find a particle at the position $\vec{x}$ when measured at time $t$ (provided the particle is prepared in the state, described by this wave function).