Some questions about the heisenberg picture

Click For Summary
SUMMARY

The Heisenberg picture in quantum mechanics (QM) involves time-dependent operators and time-independent eigenvalues. Probabilities for measuring eigenvalues are calculated using these operators, which encapsulate the initial conditions of the system. The eigenvectors are indeed time-dependent, reflecting the evolution of the operators over time. For thorough examples, users can refer to the provided lecture notes from Utah State University, which offer detailed insights into the Heisenberg picture.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with eigenvalues and eigenvectors
  • Knowledge of operator theory in quantum mechanics
  • Basic grasp of time evolution in quantum systems
NEXT STEPS
  • Study the time evolution of operators in the Heisenberg picture
  • Explore detailed worked examples of quantum mechanics problems
  • Review the lecture notes from Utah State University on quantum mechanics
  • Learn about the mathematical formulation of quantum mechanics, focusing on operators
USEFUL FOR

Students of quantum mechanics, physicists interested in operator theory, and anyone seeking to deepen their understanding of the Heisenberg picture in quantum mechanics.

HomogenousCow
Messages
736
Reaction score
213
I have some questions regarding the Heisenberg picture of QM.
1. How does one calculate probabilities for measuring eigenvalues? Are the eigenvectors simply time dependent?
2.Does this mean for initial value problems, the initial data of the system is contained in the operators? (Or equivalently the initial values of their time dependent eigenvectors)
3.Could someone link me to some thorough worked examples of problems in the Heisenberg picture, the ones readily available over google tend to be short and unsatisfying.
Thanks

Edit: Found some good lecture notes for #3
Here's the link of anyone wants them http://www.physics.usu.edu/torre/Quantum Mechanics/6210_Spring_2008/Lectures/15.pdf
 
Last edited:
Physics news on Phys.org

Similar threads

Undergrad Quantum Measurement under Heisenberg Picture?
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Heisenberg picture and Path integrals (Zee QFT)
  • · Replies 15 ·
Replies
15
Views
3K
Graduate Expectation value in Heisenberg picture: creation and annihilation
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Asymptotic states in the Heisenberg and Schrödinger pictures
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Heisenberg/Schrodinger pictures versus passive/active
  • · Replies 10 ·
Replies
10
Views
3K
Graduate Instantaneous eigenstates in the Heisenberg picture
  • · Replies 9 ·
Replies
9
Views
4K
Graduate What is the quantum picture of laser field accelerating free electrons?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Interpretation of QM in the Heisenberg Picture
  • · Replies 34 ·
2
Replies
34
Views
6K
Undergrad How to add time variation to a Schrodinger operator?
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Time correlation of an observable in the Schrödinger picture
  • · Replies 6 ·
Replies
6
Views
2K