Question

How can the wave function be represented this way.

Answer 1

$$\huge \psi = e^{\ i(kx-\omega t)} $$

Answer 2

This is just another way of writing a sinusoidal varying function. In this case it would represent a free particle. Sometimes it is mathematically advantageous to use this form instead of sines and cosines.

Answer 3

I want to proof. I know this.. Can you provide me any link or any pages you know where the proof is maintained.

Answer 4

# i know this is a way of writing the sine variation

Answer 5

This ploy of using complex notation vis-a vis trigonometric notation is common in electromagnetic wave theory. the relationship between exponential and trigonometric functions is called Euler's formula. see http://en.wikipedia.org/wiki/Euler%27s_formula
for a proof.