Any quick help with rearranging schrodinger equation in dirac notation

Click For Summary
SUMMARY

The discussion focuses on rearranging the Schrödinger equation in Dirac notation, particularly in the context of relativistic corrections and perturbation theory applied to hydrogen. The user expresses confusion regarding the treatment of the Coulomb potential, specifically the sign of the potential when moved across the equation. It is established that the Coulomb potential, represented as V(r) = e²/(4πε₀r), is indeed a repulsive potential, and the user suggests a possible typo in the initial substitution that should include a negative sign for an attractive potential.

PREREQUISITES
  • Understanding of Schrödinger equation in quantum mechanics
  • Familiarity with Dirac notation
  • Knowledge of perturbation theory
  • Basic concepts of Coulomb potential in quantum systems
NEXT STEPS
  • Review the derivation of the Schrödinger equation in Dirac notation
  • Study the principles of perturbation theory in quantum mechanics
  • Examine the properties of Coulomb potentials and their implications in quantum systems
  • Investigate common typographical errors in quantum mechanics equations
USEFUL FOR

Students and educators in quantum mechanics, particularly those studying relativistic effects and perturbation theory, as well as researchers focusing on the mathematical formulation of quantum systems.

Dmon1Unlimited
Messages
1
Reaction score
0
I'm looking through my lecture notes, (studying relativistic corrections/perturbation theory using hydrogen), and I seem to have a mind block with one of the equations (the last one from the 3 in the middle).

I know that the kinetic energy and coulomb potential has been subbed in for the operator H0, but I don't understand the rearrangement. Simply multiply both sides by 2*m, then take the coulomb potential to the other side.

The coulomb potential (the e^2 term) on the left hand side is positive, moving it to the right would make it negative, so why is it positive?
 

Attachments

  • 1.jpg
    1.jpg
    32.1 KB · Views: 535
Physics news on Phys.org
I know that the kinetic energy and coulomb potential has been subbed in for the operator H0, but I don't understand the rearrangement. Simply multiply both sides by 2*m, then take the coulomb potential to the other side.
... I think I see what you mean.
##V(r)=e^2/4\pi\epsilon_0r## would be a repulsive potential wouldn't it?
If the potential is supposed to be attractive, then they've made a typo in the initial substitution: there should be a minus sign in there.
 

Similar threads

MATLAB Code: Stationary Schrodinger EQ, E Spec, Eigenvalues
  • · Replies 1 ·
Replies
1
Views
3K
Dirac Notation and Hermitian operators
  • · Replies 12 ·
Replies
12
Views
4K
Undergrad Matrix Notation for potential in Schrodinger Equation
  • · Replies 6 ·
Replies
6
Views
2K
How Is Spin-Orbit Coupling Derived from the Dirac Equation?
  • · Replies 5 ·
Replies
5
Views
2K
Schrodinger equation for step potential
  • · Replies 4 ·
Replies
4
Views
2K
Schrodinger equation for a weird potential
  • · Replies 3 ·
Replies
3
Views
2K
What Are the Positive and Negative Energy Solutions of the Dirac Equation?
  • · Replies 1 ·
Replies
1
Views
2K
Klein-Gordon-Schrodinger and Dirac equations
  • · Replies 2 ·
Replies
2
Views
4K
Integrating the time-indepdent Schrodinger equation
  • · Replies 2 ·
Replies
2
Views
2K
Quantum Mechanics: Substitution and Coulomb Potential in Schrodinger Equation
  • · Replies 1 ·
Replies
1
Views
2K