Quantum Mechanics: Hydrogen atom in an Electric field

Click For Summary
SUMMARY

The discussion focuses on the application of perturbation theory to a hydrogen atom subjected to an external electric field, specifically using the perturbation Hamiltonian H' = -eE_{ex} * z. The problem is derived from Griffiths' "Introduction to Quantum Mechanics," 1st edition, Problem 6.31. Participants emphasize the importance of calculating the expectation value of z to find the energy correction. The approach involves integrating the wave functions of the hydrogen atom in the presence of the electric field.

PREREQUISITES
  • Understanding of perturbation theory in quantum mechanics
  • Familiarity with the hydrogen atom wave functions
  • Knowledge of expectation values in quantum mechanics
  • Basic principles of electric fields and their effects on atomic systems
NEXT STEPS
  • Study perturbation theory applications in quantum mechanics
  • Learn how to calculate expectation values for hydrogen atom wave functions
  • Explore the effects of external electric fields on atomic energy levels
  • Review Griffiths' "Introduction to Quantum Mechanics" for additional problems and solutions
USEFUL FOR

Students and professionals in physics, particularly those studying quantum mechanics, as well as educators looking for problem-solving techniques related to perturbation theory and atomic interactions with electric fields.

ArjSiv
Messages
5
Reaction score
0
So, we have an external electric field E_{ex} being subjected to a hydrogen atom and thus adding the following term to the perturbation:

H^{'} = -e\vec{E_{ex}} \cdot r.

The first question asks to find the correction to the energy treating it as a perturbation, and hints to use the external field being in the Z direction. So... I have absolutely no idea how to approach this problem other than having H^{'} = -eE_{ex} * z, but I have no idea where to go from here.

This problem can't be that difficult, I'm just stumped as to where to go from here.

By the way, this problem is from Griffiths 1st ed, Problem 6.31

Thanks in advance!
 
Physics news on Phys.org
Are you somehow stuck with the integration when you try to calculate the expectation value of z? Your choice of perturbation is correct.
 

Similar threads

Electric sinusoidal field on a hydrogen atom - Quantum Mechanics
  • · Replies 3 ·
Replies
3
Views
2K
Spin-Orbit Coupling in Hydrogen Atom: Understanding the Calculation
  • · Replies 6 ·
Replies
6
Views
4K
Electric field of a neutral conductor just at the surface
  • · Replies 4 ·
Replies
4
Views
2K
Hydrogen Atom in an electric field along ##z##
  • · Replies 0 ·
Replies
0
Views
2K
Potential difference defined in non-conservative electric field
  • · Replies 12 ·
Replies
12
Views
2K
Find the possible outcomes of ]##L^2## and ##L_{z}##
  • · Replies 21 ·
Replies
21
Views
2K
Hydrogen Ionization Rates Using Time Dependent Perturbation
  • · Replies 1 ·
Replies
1
Views
3K
Probability of the outcomes of ##J^2## and ##J_{z}##?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Why is m_j not a good quantum number in strong-field Zeeman effect?
  • · Replies 2 ·
Replies
2
Views
2K
Adiabatic Approximation in Hydrogen Atom
  • · Replies 6 ·
Replies
6
Views
2K