Question about measuring physcial observables

  • Context: Graduate 
  • Thread starter Thread starter cragar
  • Start date Start date
  • Tags Tags
    Measuring observables
Click For Summary
SUMMARY

The discussion centers on the measurement of physical observables in quantum mechanics (QM), specifically focusing on eigenvalues and expectation values. It is established that while the measurement of a quantum system yields an eigenvalue of an operator, the exact eigenvalue cannot be predicted even with a known state vector. The expectation value, calculated from an infinite number of measurements, may not correspond to a measurable eigenvalue. The conversation also touches on the definition of physical observables and the nature of their infinite possibilities.

PREREQUISITES
  • Understanding of quantum mechanics fundamentals
  • Familiarity with eigenvalues and operators in QM
  • Knowledge of expectation values in statistical mechanics
  • Basic grasp of measurement theory in quantum systems
NEXT STEPS
  • Study the concept of eigenvalues and eigenvectors in quantum mechanics
  • Research the mathematical formulation of expectation values in QM
  • Explore the implications of measurement theory in quantum systems
  • Investigate the classification and nature of physical observables in quantum mechanics
USEFUL FOR

Students and enthusiasts of quantum mechanics, physicists exploring measurement theory, and researchers interested in the foundational aspects of quantum observables.

cragar
Messages
2,546
Reaction score
3
So my measurement of a quantum system is an eigenvalue of that operator.
And we are not able to predict what eigenvalue we will get, even if we knew the precise state vector before we make our measurement. But QM allows us to calculate the average of all these eigenvalues, if we made an infinite amount of measurements and then took the average. And we call this the expectation value. So the expectation value that we calculate might not even be a possible eigenvalue that we could measure?
Im just starting to learn QM. Any input will be much appreciated.
 
Physics news on Phys.org
cragar said:
So the expectation value that we calculate might not even be a possible eigenvalue that we could measure?

Correct.
 
ok thanks for your answer. Do we just define what physical observables are and then think of ways to measure these quantities that we defined. Or does nature have infinite amount of physical observables.
 

Similar threads

Undergrad Confused about the spectrum of an observable
  • · Replies 4 ·
Replies
4
Views
1K
Graduate Eigenvalue Problem of Quantum Mechanics
  • · Replies 6 ·
Replies
6
Views
3K
High School Extremely elementary questions about QM
  • · Replies 24 ·
Replies
24
Views
3K
Undergrad Is there a reason eigenvalues of operators correspond to measurements?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad QM: I as an Observable & Its Eigenvectors & Eigenvalue
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad States and observables in quantum mechanics
  • · Replies 5 ·
Replies
5
Views
1K
Graduate The eigenvalue power method for quantum problems
  • · Replies 2 ·
Replies
2
Views
2K
High School A stupidly basic question about expectation value
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Measurement and the Conservation of Momentum
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Can entanglement be detected in a single Bell pair?
  • · Replies 1 ·
Replies
1
Views
2K