# Wave functions

1. Mar 17, 2012

### johann1301

With the number i, its possible to create a wave function with just one variable.

example:

f(x)=i^x

or..

f(x)=2^ix

But is there any wave function without the number i AND with only one(x and y) variable? can this be created?

Last edited: Mar 17, 2012
2. Mar 17, 2012

### ckaspereli

y = sin(x)

3. Mar 17, 2012

### emailanmol

Hello,

Are you aware of the general equation of a wave?

Hint: (It is a second order differential equation)

4. Mar 18, 2012

### chiro

If you want something that oscillates, then something of the form r(x)e^(ig(x)) will give you that. A standard linear wave will be in the form g(x) = wx + c corresponding to a shift and frequency information and if you want a 'real' waveform with the same peak and trough for every wavefront then r(x) = c.

This expression will give you a complex wave-form with a real and imaginary component and if you want one or the other and not both you need to use the normal identities to get rid of the i term or the real term.

5. Mar 18, 2012

### HallsofIvy

Staff Emeritus
In fact, it is possible to construct a one-dimensional wave of any shape.

6. Mar 19, 2012

### johann1301

This is the same as

y=1/2 i e^(-i x)-1/2 i e^(i x)

so that would be "cheating"...

Last edited: Mar 19, 2012
7. Mar 19, 2012

### johann1301

does this mean i*g(x) (the imaginary unit times the function g of x)?

8. Mar 19, 2012

### johann1301

I dont know anything about differential equations:(