What is the energy of a particle

  • Context: Graduate 
  • Thread starter Thread starter jaydnul
  • Start date Start date
  • Tags Tags
    Energy Particle
Click For Summary
SUMMARY

The energy of a particle in quantum mechanics (QM) is determined by the Hamiltonian, which for a hydrogen atom includes kinetic energy and electric potential energy. The energy eigenvalues obtained from standard QM calculations do not account for thermal energy, as thermal energy pertains to systems of many particles rather than individual particles. To incorporate mass-energy, one can manually add mc² to the Hamiltonian, or utilize relativistic quantum mechanics, which inherently includes mass-energy in its calculations.

PREREQUISITES
  • Quantum Mechanics (QM) fundamentals
  • Understanding of Hamiltonian mechanics
  • Relativistic Quantum Mechanics principles
  • Basic concepts of thermal energy in statistical mechanics
NEXT STEPS
  • Study the Hamiltonian formulation in quantum mechanics
  • Explore the principles of relativistic quantum mechanics
  • Learn about energy eigenvalues in quantum systems
  • Investigate the relationship between thermal energy and particle systems
USEFUL FOR

Physicists, quantum mechanics students, and researchers interested in the energy dynamics of particles and the implications of relativistic effects in quantum systems.

jaydnul
Messages
558
Reaction score
15
When we do a standard QM calculation we get energy eigenvalues. So, for example in the ground state of a hydrogen atom, does that energy value include the mass-energy of the particle. Does it include the thermal energy? Or is it just the kinetic plus potential energy?
 
Physics news on Phys.org
It includes whatever is included in the Hamiltonian. For the most basic hydrogen atom this is just kinetic energy and electric potential energy.

Note that thermal energy is not a property of individual particles. Thermal energy in thermodynamics or statistical mechanics is part of an approximate description of systems of many particles.
 
I see. Thanks
 
You could add the mass-energy manually (just by adding mc^2 to the Hamiltonian).

If you calculate the energy with relativistic quantum mechanics, you automatically include the mass-energy in the Hamiltonian.
 

Similar threads

  • · Replies 29 ·
Replies
29
Views
3K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 4 ·
Replies
4
Views
1K
  • · Replies 75 ·
3
Replies
75
Views
5K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 16 ·
Replies
16
Views
1K
  • · Replies 29 ·
Replies
29
Views
2K
  • · Replies 17 ·
Replies
17
Views
1K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K