General solution of the Schrodinger equation for a free particle?

[21joanna12]

Homework Statement

I'm trying to figure out how the general solution of the Schrödinger equation for a free particle when v=0 relates to anything I have learned in class...

Homework Equations

For Eψ=(hbar²/2m)d²ψ/dx₂

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

 

[ehild]

Homework Statement

I'm trying to figure out how the general solution of the Schrödinger equation for a free particle when v=0 relates to anything I have learned in class...

Homework Equations

For [STRIKE]Eψ=(hbar²/2m)d²ψ/dx₂
[/STRIKE]

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

 

[haruspex]

That is a differential equation of form y"+kx=0.

y"+ky=0?

 

[ehild]

I meant it so. Thanks.

ehild