I am studying a book (Engineering Physics by P.Khare & A.Swarup) on Schrodinger Wave function. I don't understand how did the text get the solution for classical wave function.

Please click on the link to view the classical wave function:
http://img23.imageshack.us/img23/1711/abcd0001vpd.jpg

The solution of the equation will be ψ(x,y,z,t) = ψ0(x,y,z) * exp(-i*w*t) according to the text.

Can anyone teach me how to reach the solution?

 

There is a derivation of the equation in post#15 of this thread.

http://forum.allaboutcircuits.com/showthread.php?t=16463&highlight=Schrodinger&page=5

The trigonometric and exponential solutions are equivalent.