2D Schroedinger eq. vs Bohr's model?

  • Thread starter arivero
  • Start date
  • Tags
    2d Model
In summary, the conversation discusses the limitations of Bohr's model in predicting the square of angular momentum for low values of n. It is also mentioned that solving the hydrogen atom potential in a 2D equation may yield different results, with energy levels depending on (n - 1/2) instead of n. Classic references are provided for further reading on this topic.
  • #1
arivero
Gold Member
3,480
164
For low values of n, Bohr's model fails to reproduce the value of the square of angular momentum, and the repulsion angles

But Bohr model is basically a planar model... so the question should be, if we solve the hydrogen atom potential in a 2D equation, is it still different? The eigenvalues of angular momentum squared, in generical dimensions, are as L(L+d-2), are they?
 
Physics news on Phys.org
  • #2
I seem to remember the quantum solutions to the 2-D hydrogen atom having energy levels that depend on (n - 1/2) rather than n.
 
  • #4
Dr. Courtney said:
depend on (n - 1/2) rather than n.
Hmm I see. Probably related to Biederharn "Sommerfeld' puzzle"

Thanks for the references, going to read them.
 

Related to 2D Schroedinger eq. vs Bohr's model?

1. How are the two models different?

The Bohr model of the atom is a simplified model that describes the structure of an atom based on the energy levels of electrons. On the other hand, the 2D Schroedinger equation is a mathematical model that accurately describes the behavior of electrons in an atom, taking into account their wave-like nature and the probability of finding them in different regions of space.

2. Which model is more accurate?

The 2D Schroedinger equation is considered to be more accurate than the Bohr model. This is because it takes into account the wave-like behavior of electrons, which is not accounted for in the Bohr model. The 2D Schroedinger equation also allows for a more precise calculation of the energy levels of electrons.

3. How does the 2D Schroedinger equation explain the stability of atoms?

The 2D Schroedinger equation explains the stability of atoms by describing the probability of finding electrons in different regions around the nucleus. In the areas of high probability, the electrons are more likely to be found, making these regions more stable. This is similar to the concept of orbitals in the Bohr model, but the 2D Schroedinger equation allows for a more detailed and accurate calculation of these regions.

4. Can the 2D Schroedinger equation be applied to all atoms?

Yes, the 2D Schroedinger equation can be applied to all atoms. It is a universal model that can accurately describe the behavior of electrons in any atom, regardless of its size or atomic number.

5. What are the limitations of the 2D Schroedinger equation?

Although the 2D Schroedinger equation is a more accurate model than the Bohr model, it still has its limitations. It does not take into account the effects of relativity and the interactions between multiple electrons. It also cannot accurately predict the exact position and momentum of an electron at the same time, due to the Heisenberg uncertainty principle.

Similar threads

The Hydrogen Atom (Schrodinger vs original Bohr theory)
Replies
1
Views
7K
I How to turn model of Schrödinger's Equation 2D?
Replies
6
Views
2K
Rutherford model of atom and Bohr model
Replies
1
Views
1K
A Renormalizability conditions for a real scalar field in d dimensions
Replies
2
Views
1K
Bohr Model missing momentum question
Replies
8
Views
3K
Bohr-Sommerfeld model question "Old" Quantum Theory
Replies
8
Views
2K
I Dot product of two vector operators in unusual coordinates
Replies
14
Views
2K
Angular momentum and the hydrogenic atom
Replies
5
Views
2K
I Exploring Microscopic Particles: Interactions & Measurement
Replies
4
Views
1K
Why did Bohr's model work for 1 electron systems?
Replies
7
Views
7K

Hot Threads

Recent Insights

Back
Top