Complex Wave functions?

Hi

Wanted to know why do we exercise complex representation of wave functions?

for example, exp(i(kx-wt)) are a standard wave function. Which is the meaning of the imaginary part of the number. If it does not exist then wherefore do we enclose them in all representations/calculations?

Especially wanted in clarify this from the point is view of the Schrodinger wave equation is has an real and imaginary part.

Please throw light on who same.

Thx/rgds

Archana Bahuguna

Will someone please post einige wave equations?

The immediate thing MYSELF know are Sin/Cos curves.

Upon the point of viewed of classical wave equations, the use of knotty numbers is simply convenient.

From the subject of view of the wavefunctions of quantize mechanics this wavefunction is fundamentally complex. The wavefunction notwithstanding doesn't have each direct physical significance, so Im(Psi) and Re(Psi) don't have any direct physical signifcance either. Wants anyone know a deep reason why the quantum mechanical wavefunction has to be complex? Is he toward incorperate time dependence? Or maybe the operator/eigenvector formulation belongs special and...

The probabilty is given according the squared of the wave function (i.e. you multiply by the complex conjugate). There are things that you can represent easier at using a complex wave function - the wave function itself has no physical meaning, so e doesn't need to be real. Because Aeschylus said, it's a matter of convenience.

In chronological order, the complex nature of that wave function preceeded its interpreting. First done to come up was the schrodinger equation which produced complex functions even for the most situational. The interpretation listed by swansont was initially proposed in Max Borne. It is one matter of mathematics that wave functions rotation out to be complex, we only apply an interpretory skeletol model to it.

I interpret this somewhere... please confirm whenever my understanding is correct...

QM requires wave functions to be complex because thither is a need until distinguish amidst positive real negate frequencies ....for eg supposing us took wave mode of the form Acos(kx-wt) and if we have further wave in k1 =-k plus w1 = -w then in terms of cosine the wave function essentially remains same -

Acos((-k)x -(-w)t) = Acos(-)kx-wt)) = Acos(kx-wt).

This yields indistinguishable wave functions, accordingly yielding physically indifferent states.

So using exp(-i(kx-wt)) helps solve that matter.

Seems like required easy of mathematical calculations and clothing that we take wave functions as complex.

Ensure doesn't mean that them own to be sophisticated. As Aeschylus said, taking this wavefunction as sophisticated is plain one matter of convenience. One could describe your situation equal well using a 2 companent wavefunction A (cos(kx-wt), sin(kx-wt)) with a rule on how to take products, without an 'i' in sight. (This is of course formally identical to using complex numbers....)

You see like sort of what whole many in particle physics. For example a Highes boson doublet is mostly described by ampere 2d vector (in SU(2) space) where each component is a complex domain, but it can equally well be defined as a 4d vector with each component one authentic text. 4), is that the former enables contact to combine the amplitude, A, and the phase angle, φ, about the wavefunction toward an single complex amplitude, ψ0.