Why Do We Need Complex Wavefunction in Quantum Mechanics?

[wasi-uz-zaman]

hi, please explain why do we need complex wavefunction in quantum mechanics?

 

[Bill_K]

hi, please explain why do we need complex wavefunction in quantum mechanics?

Interference. Complex amplitudes are necessary to produce interference.

 

[bhobba]

Check out the following:
http://www.scottaaronson.com/democritus/lec9.html

See the section real vs complex numbers.

Thanks
Bill

 

[dauto]

hi, please explain why do we need complex wavefunction in quantum mechanics?

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.

 

[Bill_K]

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.

 

[Naty1]

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:

..yet with all the structures mathematicians studied, none of them came up with quantum mechanics until experiment forced it on them...

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 cool person 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...


Brian Greene:

The telltale difference between quantum and classical notions of probability is that the former is subject to interference and the latter is not.

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...

..Either we do physics on a large scale, in which case we use classical level physics; the equations of Newton, Maxwell or Einstein and these equations are deterministic, time symmetric and local. Or we may do quantum theory, if we are looking at small things; then we tend to use a different framework where time evolution is described... by what is called unitary evolution...which in one of the most familiar descriptions is the evolution according to the Schrödinger equation: deterministic, time symmetric and local. These are exactly the same words I used to describe classical physics.

However this is not the entire story... In addition we require what is called the "reduction of the state vector" or "collapse" of the wave function to describe the procedure that is adopted when an effect is magnified from the quantum to the classical level...quantum state reduction is non deterministic, time-asymmetric and non local...The way we do quantum mechanics is to adopt a strange procedure which always seems to work...the superposition of alternative probabilities involving w, z, complex numbers...an essential ingredient of the Schrödinger equation. When you magnify to the classical level you take the squared modulii (of w, z) and these do give you the alternative probabilities of the two alternatives to happen...it is a completely different process from the quantum (realm) where the complex numbers w and z remain as constants "just sitting there"..

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.

 

[ChrisVer]

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.

physics of waves!