# Exponential formulation of waves

1. Dec 25, 2013

### 11thHeaven

Hi all, I'd just like to clear up something that's often confused me.

In classes (particularly classical waves/QM) we've often seen the lecturer switch from describing a wave as (most commonly) $$Acos(kx-{\omega}t)$$ to $$e^{i(kx-{\omega}t)}$$
but doesn't the exponential representation include an imaginary sine term as well? Shouldn't this given wave be represented as ( $$Re [e^{i(kx-{\omega}t)}]$$)?

If this is the case, is it just a convention that the "Re" is dropped?

Thanks.

2. Dec 25, 2013

### Pythagorean

As far as I've seen, yes, it's just convention.

3. Dec 27, 2013

### Redbelly98

Staff Emeritus
For classical waves (like E-M waves), yes, it's generally understood that the real part of the expression gives the physical wave (like the electric field value).

For wavefunctions in quantum mechanics, the imaginary part is really part of the wavefunction. All the operations used to find an observable quantity (energy, momentum, probability) from the complex wavefunction still give real-valued results.