Wavefunction really like a wave?

[venton]

Is the wavefunction of a particle really shaped like a wave? A lot of analogies are made about how the wave function is like a water wave which can interfere with other waves.
But does the Schrödinger equation truly produce something shaped like a wave (ie a 3d sine wave) when plotted?

 

[nnnm4]

Particle localized in a finite box gives 3d sine waves.

 

[venton]

Thanks. How come that when a photon goes through a single slit that the wavefunction doesn't spread out, and the particle appears randomly anywhere along the spread out wave?
Instead it appears to go through the slit as a particle and appears as single spot.
I am imagining there is literally one slit here, not two.

 

[javierR]

Whether there is a single open slit or a double-slit setup, there will be an interference pattern due to a single particle (e.g. photon) as long as the setup has no detector to find out where the particle is until the end of the experiment. For the single slit case, if you measure the position of the particle the waveform describing it is changed such that the diffractive interference effects are diminished. The resulting uncertainty in the momentum means there is a spread in the possible ending position of the particle...just that it'll look more like a lump rather than and inferference pattern. Going the other way, the less precisely we detemine the position of the particle passing through the slit, the greater the resulting diffractive interference effects.