Calculating Hamiltonian for H-Atom & Energy Changes in Magnetic Field

  • Thread starter Thread starter hdsncts
  • Start date Start date
  • Tags Tags
    Hamiltonian
Click For Summary
SUMMARY

The discussion focuses on calculating the Hamiltonian for a hydrogen atom in an external magnetic field and determining the energy changes (deltaE) for the orbitals Y01, Y11, and Y-11. Participants emphasize the importance of understanding the Hamiltonian operator, which consists of a constant term and an environment-dependent term. The conversation highlights the need for clarity in notation for orbitals, as variations exist between different educational contexts. Participants seek guidance on how to approach the problem and interpret the results related to wavefunction time-evolution.

PREREQUISITES
  • Understanding of Hamiltonian operators in quantum mechanics
  • Familiarity with hydrogen atom wavefunctions and their notations
  • Knowledge of external magnetic fields and their effects on atomic systems
  • Basic principles of quantum mechanics, including time-evolution of wavefunctions
NEXT STEPS
  • Study the derivation of the Hamiltonian for a hydrogen atom in external fields
  • Learn about the Zeeman effect and its implications for energy levels
  • Explore the mathematical representation of wavefunctions for hydrogen orbitals
  • Investigate the time-evolution operator in quantum mechanics
USEFUL FOR

Students of quantum mechanics, physicists working with atomic systems, and educators seeking to clarify concepts related to Hamiltonians and magnetic fields in atomic physics.

hdsncts
Messages
10
Reaction score
0

Homework Statement


Write down the full Hamiltonian for a hydrogen atom in an external field. Next, calculate the energy changes deltaE (not absolute E) of the three orbitals Y01, Y11, and Y-11 induced by the applied magnetic field Bz. Interpret your results with respect to your knowledge of the time-evolution of the wavefunctions.




Homework Equations





The Attempt at a Solution


In all honesty I have no idea how to start this. I know what a Hamiltonian operator is but that's about it. I understand that this forum isn't so that other people can do my homework for me, so can someone help me start in the right direction? Any help would be greatly appreciated.
 
Physics news on Phys.org
If you know what a Hamilitonian is, you'll know that half of it is the same for everything, and the other half is dependent on the environment. Which is which, and which half is dependent on the environment?

Also, can I clear up how your notation for orbitals works? Looks like it might be different from the one used in my course last year.
 

Similar threads

Plane pendulum: Lagrangian, Hamiltonian and energy conservation
  • · Replies 6 ·
Replies
6
Views
4K
How does spin magnetization affect energy configurations in non-ideal systems?
  • · Replies 1 ·
Replies
1
Views
2K
Eigenvalues dependent on choice of $\vec{A}$?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Hamiltonian of a particle in a magnetic field
  • · Replies 10 ·
Replies
10
Views
4K
Spin-Orbit Coupling in Hydrogen Atom: Understanding the Calculation
  • · Replies 6 ·
Replies
6
Views
4K
Solve Problem: Partition Function for Magnetic Moment
  • · Replies 2 ·
Replies
2
Views
2K
Time Evolution of Spin in a Magnetic Field
  • · Replies 1 ·
Replies
1
Views
3K
Orthonormality and the Stark Effect
  • · Replies 2 ·
Replies
2
Views
2K
Are Electronic States in a 1D Atomic Chain Eigenstates of the Hamiltonian?
  • · Replies 1 ·
Replies
1
Views
2K
How Many Beams Are Hydrogen Atoms Deflected Into in a Magnetic Field?
  • · Replies 12 ·
Replies
12
Views
5K