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Are there any examples in the history of physics where a phenomenon was considered by the physics community to be not explainable by classical physics and needed a quantum explanation whereas some time later it was noticed that this claim was wrong (perhaps because for instance one "over-idealized" the system, neglected boundary effects or did some other mistakes when "proofing" that there is no classical explanation), i.e. that the phenomenon has indeed a classical explanation? Let me call those effects "pseudo quantum effects" for short.

Are there such pseudo quantum effects which were today common misconceptions (i.e. where people think that one needs a quantum description but doesn't really do it...)

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I think Rashba splitting is such a phenomenon. You can read the following article on arxiv arxiv.org/pdf/cond-mat/0407247‎ which succeeded to explain it classically. –  Mathusalem Jun 15 '13 at 11:20
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classical and semi-classical descriptions can give descriptions that are indistinguishable from quantum results at a given experimental accuracy; eg violations of Bell's inequality can be created classically via sampling bias due to threshold detectors; this loophole has (afaik) been closed experimentally, but only fairly recently (which makes this a counter example and thus not an answer to your question); in a similar vein, Khrennikov is developing a classical formalism that approximates quantum mechanics, but leads to a modified Born's rule; –  Christoph Jun 15 '13 at 13:45

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I think photoelectric effect is a good example. Before formal quantum mechanics(e.g. Schrodinger's equation) was developed, it was believed the effect was due to the quantum nature of light. However, just using Schrodinger's equation+perturbation theory+classical EM wave it is sufficient to demonstrate the existence of photoelectric effect(the electron is still treated quantum mechanically though).

To be brief, perturbation calculation shows that in the presence of a classical EM wave $\vec{E_0}\cos(\vec{k}\cdot\vec{r}-\omega t)$, the transition rate between two energy levels of the atomic system is proportional to $\delta(E_f-E_i-\hbar\omega)$. So photoelectric effect is really just a resonance effect, and should not be taken as a robust evidence of the existence of photons.

More details about the calculation: The photoelectric effect

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No, this is incorrect. Here is an analysis: physicsforums.com/showthread.php?t=372653 –  Ben Crowell Jun 15 '13 at 15:10
    
I can't access the Lamb&Scully paper, is their argument essentially the same as the link I quoted? You said "Therefore if a single photon illuminates the cathode, it may ionize more than one atom, violating conservation of energy", can you elaborate this? At least I can't see anything about energy conservation issue in the link I quoted. –  Jia Yiyang Jun 15 '13 at 16:06
    
A pdf of the Lamb-Scully paper can be found online by googling. I've started a separate question about this: physics.stackexchange.com/q/68147/4552 –  Ben Crowell Jun 15 '13 at 16:34
    
Not having read the paper, I don't want to be too definitive, but it seem to me that getting a absorption probability proportional to a delta function in energy doesn't explain the photoelectric effect in any case. It get's the threshold right but fails to explain the above threshold behavior (where quantum mechanics still has a non-zero interaction probability generating the linear relationship between stopping potential and excess photon energy seen experimentally). –  dmckee Jun 15 '13 at 16:42
    
@BenCrowell: I'm not quite convinced. In deriving a delta function out of the perturbation theory, one has to take the $t\to\infty$ limit, and if taken literally, this means we are considering the case where the external EM wave gives an infinite energy supply. –  Jia Yiyang Jun 16 '13 at 0:14

The "quantum mind" assumption springs to mind. This assumption goes back to Bohm. More recently Penrose has defended a similar position. Yet, nowadays very few physicists would support a brain at 310 K to operate in a quantum coherent way.

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I don't believe Bohr actually made this assumption. Any evidence for this? –  Peter Shor Jul 15 '13 at 14:43
    
No other evidence than the statement in the Wikipedia article. This statement lacks support by any reference, so have deleted the reference to Bohr in the above. Thanks for notifying me on this. –  Johannes Jul 15 '13 at 14:49

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