Schrodinger equation and boundary conditions

In summary, the conversation discusses the use of boundary conditions for solving the Schrodinger equation in spherically symmetric systems. These boundary conditions involve the function u(r) and its derivative, which must approach zero at the boundaries of integration. The reason for this is influenced by the potential function V(r), which can affect the nature of the solution. The harmonic oscillator potential and Woods-Saxon potential are examples of potential functions that can be used.
  • #1
BRN
108
10
Hi at all,
I'm tring to solve Schrodinger equation in spherically symmetry with these bondary conditions:

##\lim_{r \rightarrow 0} u(r)\ltimes r^{l+1}##
##\lim_{r \rightarrow 0} u'(r)\ltimes (l+1)r^{l}##

For eigenvalues, the text I'm following says that I have to consider that the eigenfunctions are tending to zero at the extremes of integration, i.e. ##r = 0## and ##r = 3 * r_{nucl}##

Why I need to consider an eigenfunction=0 in r=0? I would expect it to be maximum at that point...

Some idea?

Thanks.
 
Physics news on Phys.org
  • #2
BRN said:
Hi at all,
I'm tring to solve Schrodinger equation in spherically symmetry with these bondary conditions:

##\lim_{r \rightarrow 0} u(r)\ltimes r^{l+1}##
##\lim_{r \rightarrow 0} u'(r)\ltimes (l+1)r^{l}##

For eigenvalues, the text I'm following says that I have to consider that the eigenfunctions are tending to zero at the extremes of integration, i.e. ##r = 0## and ##r = 3 * r_{nucl}##

Why I need to consider an eigenfunction=0 in r=0? I would expect it to be maximum at that point...

Some idea?

Thanks.
What is the potential ##V(r)?## In general, if you change the function ##V## you can/will change the nature of the solution ##u(r)##.
 
  • #3
Now, I'm using the harmonic oscillator potential:
##
\frac{1}{2}m \omega^2r^2
##

But these boundary conditions are used for Woods-Saxon potential too.
 

1. What is the Schrodinger equation?

The Schrodinger equation is a mathematical equation that describes the behavior of quantum mechanical systems, such as the motion of particles at the atomic and subatomic level.

2. What are boundary conditions in the Schrodinger equation?

Boundary conditions refer to the constraints placed on the wave function in the Schrodinger equation, which determine the behavior of the system at the boundaries of the region in which it exists.

3. Why are boundary conditions important in the Schrodinger equation?

Boundary conditions are important because they allow us to determine the behavior of a quantum system in a specific region. They also help us to determine the possible values of physical quantities, such as energy and momentum, for the system.

4. What are the types of boundary conditions in the Schrodinger equation?

There are two main types of boundary conditions in the Schrodinger equation: hard and soft boundaries. Hard boundaries are those where the wave function must be equal to zero, while soft boundaries allow for finite values of the wave function at the boundary.

5. How are boundary conditions determined in the Schrodinger equation?

Boundary conditions are typically determined by the physical properties of the system and the environment in which it exists. They can also be determined by experimental observations or theoretical considerations.

Similar threads

Replies
0
Views
418
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
272
  • Calculus and Beyond Homework Help
Replies
9
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
901
Replies
2
Views
718
  • Calculus and Beyond Homework Help
Replies
1
Views
912
  • Advanced Physics Homework Help
Replies
4
Views
957
  • Calculus and Beyond Homework Help
Replies
2
Views
667
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
Back
Top