Solving radial wavefunction in odd central potential

In summary, the author is trying to solve a radial wave equation using a trick that has been used before, but the equation is hard to read. The form of the potential is unknown, but it is related to the central gravitational potential in a non-Newtonian way.
  • #1
FunkyDwarf
489
0
Hey guys,

I have a question regarding solving a radial wavefunction DE which i have written up in Mathematica and saved as a pdf http://members.iinet.net.au/~housewrk/PFpost.pdf" as I was already doing the work in MM and writing it all up again in LaTeX seemed a bit of a waste of time.

If anything is not clear or wrong or whatever please let me know and i will respond as best i can =D

Cheers
-G
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
FunkyDwarf said:
Hey guys,

I have a question regarding solving a radial wavefunction DE which i have written up in Mathematica and saved as a pdf http://members.iinet.net.au/~housewrk/PFpost.pdf" as I was already doing the work in MM and writing it all up again in LaTeX seemed a bit of a waste of time.

If anything is not clear or wrong or whatever please let me know and i will respond as best i can =D

Cheers
-G

The math in that document is completely unreadable ... but regardless, can't you use the usual trick of multiplying the radial wavefunction by r (or some other simple function) to wipe out the pole at r=0? What is the form of your central potential? Knowing that might help to analyze the asymptotic limit you are after.
 
Last edited by a moderator:
  • #3
Yeah sorry, i should have been more mindful of the margins. Like i said, I've tried several function substitutions including that usual trick; i still end up with an r dependence in the denominator for the coefficient of R(r). The form of the central potential is unknown, if i knew that i could probably do some usual wave scattering things. This radial equation was derived from solving the Klein Gordon equation in the interior Schwarzschild metric, so it is 'like' a central gravitational potential, but not in a Newtonian sense.

I have updated that pdf in an attempt to make it more readible, but let's be fair, that equation is a piece of **** to read anyway you write it :)
 

Related to Solving radial wavefunction in odd central potential

1. What is a radial wavefunction in the context of odd central potential?

A radial wavefunction is a mathematical function that describes the probability amplitude of a particle being at a certain distance from the center of an odd central potential. It is an essential tool in solving the Schrödinger equation for systems with spherical symmetry.

2. How do you solve for the radial wavefunction in odd central potential?

The radial wavefunction can be solved using various techniques, such as the separation of variables method or the power series method. These methods involve manipulating the Schrödinger equation and applying boundary conditions to obtain a solution.

3. What are some common odd central potentials that require solving for the radial wavefunction?

Some common odd central potentials include the Coulomb potential, the linear potential, and the harmonic oscillator potential. These potentials are often encountered in quantum mechanics and have different mathematical forms that require different methods for solving the radial wavefunction.

4. What role does the radial wavefunction play in determining the energy levels of a system?

The radial wavefunction is a key factor in determining the energy levels of a system with an odd central potential. The energy levels are directly related to the solutions of the radial wavefunction, and the shape of the potential also affects the energy levels of the system.

5. How does the oddness of the central potential affect the solutions for the radial wavefunction?

The oddness of the central potential has a significant impact on the solutions for the radial wavefunction. In odd central potentials, the solutions are typically asymmetric and can have nodes, unlike even central potentials where the solutions are symmetric. This difference leads to different energy level patterns and behavior for particles in odd and even central potentials.

Similar threads

A Solving the Radial Equation for the Dirac Hydrogen Atom Solution
    • Quantum Physics
Replies
10
Views
2K
Why Does the Neumann Function Get Discarded in Free Particle Solutions?
    • Quantum Physics
Replies
1
Views
2K
How Do Numerical and Analytical Solutions Compare in Finite Coulomb Problems?
    • Quantum Physics
Replies
1
Views
2K
How Does the Wavefunction Behave at an Infinite Potential Barrier?
    • Quantum Physics
Replies
4
Views
8K
Many body wavefunction and exchange correlation
    • Atomic and Condensed Matter
Replies
1
Views
2K
Solving Coulomb Potential with Schrodinger Equation - Roger Newton & Mathematica
    • Quantum Physics
Replies
1
Views
4K
Determine the potential V(x) from the Hamiltonian
    • Advanced Physics Homework Help
Replies
3
Views
2K
Solving for Particle Trajectory in Central Potential with Initial Conditions
    • Advanced Physics Homework Help
Replies
1
Views
2K
The reality of Configuration space
    • Quantum Physics
3
Replies
94
Views
25K
Mathematica [Mathematica] NDsolve eating stacks of RAM
    • MATLAB, Maple, Mathematica, LaTeX
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top