Question

oh wavefunctions. why do you mock me?

Answer 1

What are you struggling with?

They aren't as bad as you might initially think. Take, for example, the harmonic wave function:

\[Asin[k(x \pm vt)] where k = 2\pi/\lambda and \omega = 2piv \]

You can think about this in two ways. First, think about a constant time so this function will give you the amplitude of the wave function at each position. Now, way number two, if you remember some basic algebra then if I add or subtract a number to the argument of a function it simply translates it to the right/left. So, as the wave moves in time it just translates the curve to the right/left and so you can simply imagine the wave at an instant of time to get the shape and then allow time to change so that it moves. This is, in essence, how the wave functions work. This works for plane waves, spherical waves, etc... Hope this helps!