hi, please explain why do we need complex wavefunction in quantum mechanics?
Interference. Complex amplitudes are necessary to produce interference.
Check out the following:
See the section real vs complex numbers.
Unless there is an specific reason to assume a quantity is real one should assume it might be complex. Arbitrarily Setting it to be real would've been an unwarranted unnecessary restriction.
That is surely one of the oddest philosophies I've ever heard. I would say quite the opposite. Nowhere in classical physics are complex numbers required. It is only when we come to Quantum Mechanics that they become indispensable.
Hi wazi...not to worry, as already noted, it is NOT obvious why such a model works.
I like the discussion from Bhobba's link, especially:
A directly observable effect of superposition is interference peaks, say from an electron wave in a double-slit experiment. The superposition principle is what allows us to model the quantum interference which we observe and also the so-called entanglement of quantum states. It is so far thought quantum states are themselves superpositions, or coherent mixtures, of other states. It models what we can observe. In a physical sense, the math explains what we observe, not precisely why.
But is there a chink in this armor? Something seems awry since QM so far does not seem to model things at below Planck scale. So maybe we are missing some representation? That's a realm of quantum gravity...
Roger Penrose made comments which correlate nicely with much of Bhobba's link.....
The following quote is from Roger Penrose [the mathematical physicist] celebrating Stephen Hawking’s 60th birthday in 1993 at Cambridge England.....he was addressing the elite of the physics world.....
It is also helpful to note we do not actually observe [detect] waves [the fields of opur models]. We observe the local excitations of such wave representations as the point particles of the standard model of particle physics.
physics of waves!
Separate names with a comma.