# General solution of the Schrodinger equation for a free particle?

## Homework Statement

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...

## 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
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## Homework Statement

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...

## 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

Last edited:
haruspex
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2020 Award
That is a differential equation of form y"+kx=0.
y"+ky=0?

ehild
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I meant it so. Thanks.

ehild