Deriving ground state electron energy using Boundary Value

Click For Summary
SUMMARY

This discussion focuses on deriving the ground state electron energy using Schrödinger's Equation, specifically addressing the Radial Equation and its application to solve for ##E_1##. Participants highlight the importance of understanding the constraints on quantum numbers, particularly the angular momentum quantum number ##l##, when the principal quantum number ##n=0##. The conversation emphasizes the need for clarity in problem statements and the significance of accurate representations in quantum mechanics exercises.

PREREQUISITES
  • Understanding of Schrödinger's Equation in quantum mechanics
  • Familiarity with quantum numbers: principal quantum number (n), angular momentum quantum number (l), and magnetic quantum number (m)
  • Knowledge of the Radial Equation and its derivation
  • Basic concepts of ground state energy in quantum systems
NEXT STEPS
  • Study the implications of quantum numbers on electron configurations in atoms
  • Explore the derivation and applications of the Radial Equation in quantum mechanics
  • Learn about the significance of boundary conditions in solving differential equations
  • Investigate the physical meaning of ground state energy and its calculation methods
USEFUL FOR

Students and professionals in physics, particularly those studying quantum mechanics, as well as educators looking to clarify concepts related to electron energy states and Schrödinger's Equation.

currently
Messages
21
Reaction score
5
Homework Statement
Derive the ground state electron energy ##E_1## based on the boundary condition of R(r) -> 0, r -> ∞ and write down the corresponding energy function, Psi. (5 points)
Relevant Equations
Schrodinger's Equation (below)
ss01.png

This is the equation given.
I attempted to use Radial Equation, obtained from separating variables, to solve for ##E_1##.
IMAG1361_2.jpg

IMAG1363_2.jpg
 

Attachments

  • IMAG1361_2.jpg
    IMAG1361_2.jpg
    25.9 KB · Views: 238
Physics news on Phys.org
currently said:
Here's the problem. the equation was stated in class to be Schrödinger's Equation.
Last problem should say: n, l, and m are arbitrary constants.

View attachment 255295

We are now in part (d) of your exercise. I can hardly read, let alone quote from your jpg.
What constraints are there on ##l##, and what does that mean when in the ground state ##n=0## ?
 
  • Like
Likes   Reactions: currently
BvU said:
What constraints are there on ##l##, and what does that mean when in the ground state ##n=0## ?
Okay, will keep in mind. Thanks!

BvU said:
We are now in part (d) of your exercise. I can hardly read, let alone quote from your jpg.
I'm slightly touched you remember which problem this is.. and I apologize for the terrible image quality! I'll be more quotable next post.
 
  • Like
Likes   Reactions: BvU

Similar threads

  • · Replies 4 ·
Replies
4
Views
1K
Replies
29
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
5K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 6 ·
Replies
6
Views
4K
  • · Replies 4 ·
Replies
4
Views
2K
Replies
0
Views
2K