Question about finding quantom numbers N_(n) for Schrodinger Eqn in 3D

In summary, the Modern Physics by Tipler (6th edition) book discusses the first excited state in section 7.1, which can be represented by E_(112 ) E_(121 ) E_(112). The process of finding the quantum numbers n_(1),n_(2),n_(3) involves choosing random values and then determining the order of energy levels. To find the 4th excited state, one can calculate the energies for nearby quantum numbers, such as E111, E112, E122, E212, etc. Then the states can be arranged according to their energy. This method can be applied for both cubic and non-cubic boxes.
  • #1
A$APFowler
1
0
I'm using the Modern Physics by Tipler (6th edition) book.
In sec 7.1 it talks about the first excited state being either E_(112 ) E_(121 ) E_(112).

My question is what is the process of finding the n_(1),n_(2),n_(3) quantum numbers ? How i understand you pick random values and from their find the order of energy levels. Can you give the process if would take of finding let's say the 4th excited state for both a cubic and non cubic box.

Thank you for your time.

PS: I apologize if my format is incorrect this is my fist post. The "_" represent subscript.
 
Physics news on Phys.org
  • #2
Well, if the energy dependence on the quantum numbers were somehow more complicated, you could for example calculate the gradient to find some minimum values, and go from there. In this case, the minimum is trivially at 1,1,1. After you have that sorted, then all you can really do is calculate the energies for nearby quantum numbers. So you'd find E111, E112, ... , E122, E212, and so on. Then you just arrange the states according to their energy.
 

Related to Question about finding quantom numbers N_(n) for Schrodinger Eqn in 3D

1. What is the Schrodinger Equation in 3D and why is it important?

The Schrodinger Equation is a mathematical equation that describes the behavior of quantum particles in a three-dimensional space. It is important because it allows us to understand and predict the behavior of these particles, which can have unique properties and behaviors that differ from classical particles.

2. What are quantum numbers and what is their significance in the Schrodinger Equation?

Quantum numbers are a set of values that describe the energy levels and spatial distribution of an electron in an atom. In the Schrodinger Equation, they are used to determine the allowed energy states and wave functions of the particle.

3. How do you find the quantum numbers Nn for the Schrodinger Equation in 3D?

The quantum numbers Nn can be found by solving the Schrodinger Equation for a given system or particle. This involves using mathematical techniques such as separation of variables and solving for the energy eigenvalues and corresponding wave functions.

4. What is the significance of the principal quantum number in the Schrodinger Equation?

The principal quantum number (n) represents the energy level of the electron in an atom. It determines the size and energy of the orbital and is used to calculate the energy of the electron in that orbital. It also determines the maximum number of electrons that can occupy that energy level.

5. How do the quantum numbers Nn relate to the shape and orientation of the electron's orbital in the Schrodinger Equation?

The quantum numbers Nn determine the shape and orientation of the electron's orbital through the azimuthal quantum number (l) and the magnetic quantum number (ml). These numbers determine the shape of the orbital (s, p, d, etc.) and the orientation of the orbital in space.

Similar threads

Three Dimensional Infinite-Potential Well Energies
    • Advanced Physics Homework Help
Replies
4
Views
9K
Mathematica This Week's Finds in Mathematical Physics (Week 261)
    • MATLAB, Maple, Mathematica, LaTeX
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top