General solution of the Schrodinger equation for a free particle?

  • Thread starter 21joanna12
  • Start date
  • #1
126
2

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
 

Answers and Replies

  • #2
ehild
Homework Helper
15,543
1,914

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:
  • #3
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
37,155
7,275
That is a differential equation of form y"+kx=0.
y"+ky=0?
 
  • #4
ehild
Homework Helper
15,543
1,914
I meant it so. Thanks.

ehild
 

Related Threads on General solution of the Schrodinger equation for a free particle?

  • Last Post
Replies
1
Views
973
  • Last Post
Replies
2
Views
1K
Replies
5
Views
1K
Replies
2
Views
1K
  • Last Post
Replies
4
Views
8K
Replies
9
Views
1K
  • Last Post
Replies
1
Views
4K
Replies
9
Views
679
Top