Calculating the expectation of a quantity using wavefunctions

Click For Summary
SUMMARY

The discussion focuses on calculating the expectation value of the potential energy (V) for a hydrogen atom using wavefunctions. The potential energy is defined as V = e²/r, leading to the conclusion that the expectation of V is -e²/a₀n². The user seeks clarification on the exact form of the unperturbed wavefunction ψ₀, which is essential for performing the expectation value calculation. It is noted that the ground state wavefunction is typically used for these computations, specifically for the quantum numbers n=1, l=0, m=0.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly wavefunctions
  • Familiarity with the hydrogen atom model in quantum mechanics
  • Knowledge of expectation values in quantum mechanics
  • Basic grasp of relativistic corrections in kinetic energy
NEXT STEPS
  • Research the general form of the hydrogen atom wavefunction, particularly for n=1, l=0, m=0
  • Study the derivation of expectation values in quantum mechanics
  • Explore the concept of relativistic corrections in quantum mechanics
  • Examine resources on the fine structure of hydrogen and its implications
USEFUL FOR

Students and professionals in physics, particularly those studying quantum mechanics, as well as researchers focusing on atomic structure and relativistic effects.

spaghetti3451
Messages
1,311
Reaction score
31
I am reading the fine structure article from Wikipedia at http://en.wikipedia.org/wiki/Fine_structure.

Under the heading 'Kinetic energy relativistic correction', we have the following:

For the hydrogen atom, V = e2/r. This implies that the expectation of V = -e2/a0n2.

Now, I know that you use the unperturbed wavefunction ψ0 to find the expectation of V, but I am not sure of the exact form of ψ0. Any help on this will be greatly appreciated.
 
Physics news on Phys.org
I need the form as I want to calculate the expectation myself. Is there a general formula for the wavefunction?
 
Usually the expectation value is computed with the ground state wavefunction. You can find the n=1, l=0, m=0 wavefunction in any book on QM.
 

Similar threads

Graduate Normalization of Morse potential wavefunctions
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Is the wavefunction subjective? How?
  • · Replies 128 ·
5
Replies
128
Views
15K
Graduate QFT with vanishing vacuum expectation value and perturbation theory
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Position representation of a wavefunction - technical issue
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad How Do Kochen-Specker Theorem and Contextuality Relate to Financial Markets?
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Nonlinear optics: electric dipole moment operator
  • · Replies 6 ·
Replies
6
Views
6K
High School Nuclear wavefunction and Bose-Einstein condensates
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Is Rest Mass a subjective quantity?
  • · Replies 3 ·
Replies
3
Views
2K
High School Could Fusion Reactions Occur Randomly in the Atmosphere or Planetary Cores?
  • · Replies 19 ·
Replies
19
Views
3K
High School Is there a Relativistic Quantum Chemistry Table?
  • · Replies 1 ·
Replies
1
Views
2K