Particle in superposition of energy eigenstates and conservation of energy.

Click For Summary
SUMMARY

The discussion centers on the implications of a particle existing in a superposition of energy eigenstates, specifically regarding energy conservation in quantum mechanics. Participants explore how energy is defined when a particle is measured in a lower energy state, questioning the total energy of the system. Key concepts include the Hamiltonian operator, the role of coherent states, and the conditions under which energy conservation holds in quantum systems. The conversation highlights that while energy is conserved, the correlations generated by measurements and interactions complicate the understanding of energy states.

PREREQUISITES
  • Quantum Mechanics fundamentals, including superposition and eigenstates
  • Understanding of the Hamiltonian operator and its role in quantum systems
  • Familiarity with coherent states and their properties in quantum optics
  • Knowledge of measurement theory in quantum mechanics, including wave function collapse
NEXT STEPS
  • Study the Hamiltonian framework in quantum mechanics, focusing on its implications for energy conservation
  • Explore coherent states and their applications in quantum optics, particularly in laser technology
  • Investigate the concept of superposition in quantum mechanics and its relation to measurement outcomes
  • Examine the implications of the many-worlds interpretation on energy conservation and system evolution
USEFUL FOR

Quantum physicists, students of quantum mechanics, and researchers interested in the foundations of quantum theory and energy conservation principles.

  • #31
K^2 said:
If you are talking about pure vs mixed states, that is exactly how you are defining your system. The distinction is only relevant statistically, and that implies an external system.
DrDu was talking about a CLASSICAL surrounding, while what you say above refers to a QUANTUM surrounding.

K^2 said:
Excited atom + ground state EM vacuum is still an eigen state of such a system.
It would be so if there was no interaction term in the Hamiltonian describing atom and EM field. But the interaction term is there, so what you say above is not correct.
 
Physics news on Phys.org
  • #32
The notion of a closed universe is quite interesting. Demystifier to expand on what you are saying, if energy eigenstates, so the different superpositions of a particle, must evolve into a coherent state, where does all this excess energy from these states go? Our universe,in accordance with things such as Pauli Exclusion can only have on outcome of a solution, and the physical existence of a particle in two different states seems impossible. Could it be that many worlds theory holds valid in that all these different energy eigenstates come together to form an infinite number of possibly universes, each branching from another, as a wave function collapses and the other superpositions become irrelevant to our world?
 

Similar threads

High School Spectral lines and superposition of states
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Relationship between Larmor precession and energy eigenstates
  • · Replies 15 ·
Replies
15
Views
3K
Graduate Energy conservation+superpositions=entanglement?
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Changing Hamiltonian with some eigenvalues constant
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Doesn't the superposition in energy violate the conservation of energy
  • · Replies 27 ·
Replies
27
Views
4K
Undergrad Linear combination of states with Pauli's principle
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Multiple questions about eigenstates and eigenvalues
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Energy measurement on superposition of states
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Matrix Notation for potential in Schrodinger Equation
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Does there exist a proof for these conjectures?
  • · Replies 2 ·
Replies
2
Views
2K