General solution of the Schrodinger equation for a free particle?

1. Jun 28, 2014

21joanna12

1. The problem statement, all variables and given/known data
I'm trying to figure out how the general solution of the Schrodinger equation for a free particle when v=0 relates to anything I have learned in class...

2. Relevant equations
For Eψ=(hbar2/2m)d2ψ/dx2

3. The attempt at a solution
I really have no idea- what is confusing me is that ψ is a function rather than a constant so I don't know how to treat it...

Thank you all for any help!

And I really apologise for the equation... I don't really understand how to use LaTeX

2. Jun 28, 2014

ehild

You miss the negative the sign: $-\hbar^2/(2m)d^2ψ/dx^2=Eψ$

That is a differential equation of form y"+kx=0. What is the solution?

The former equation is the time independent equation for one dimension. The time dependent equation is

$i\hbar \frac{\partial ψ}{\partial t}=-\hbar^2/(2m)\frac{\partial^2}{\partial x^2}$

ehild

Last edited: Jun 28, 2014
3. Jun 28, 2014

haruspex

y"+ky=0?

4. Jun 28, 2014

ehild

I meant it so. Thanks.

ehild