What is the Modulus of an Eigenvalue?

  • Context: High School 
  • Thread starter Thread starter dimensionless
  • Start date Start date
  • Tags Tags
    Eigenvalue Modulus
Click For Summary

Discussion Overview

The discussion revolves around the concept of the modulus of an eigenvalue, particularly in the context of quantum mechanics. Participants explore definitions and implications of modulus in both real and complex numbers, as well as its relevance to quantum mechanics and hermitian operators.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants define the modulus of a real number as its absolute value and suggest that in quantum mechanics, eigenvalues are typically real.
  • Others propose that the modulus of a complex number can be understood as its length when viewed as a vector in the plane, aligning with algebraic definitions.
  • A participant challenges the attribution of the "little arrows" concept to Feynman, suggesting it should be credited to Argand, while acknowledging Feynman's reference to complex amplitudes.
  • One participant expresses that the question seems meaningless in the context of quantum mechanics, arguing that hermitian operators have real eigenvalues, thus questioning the relevance of discussing modulus for negative eigenvalues.

Areas of Agreement / Disagreement

Participants express differing views on the relevance and interpretation of modulus in the context of quantum mechanics, with no consensus reached on the implications of eigenvalues and their modulus.

Contextual Notes

Some assumptions about the nature of eigenvalues in quantum mechanics and the definitions of modulus may not be fully articulated, leading to potential misunderstandings regarding the application of these concepts.

dimensionless
Messages
461
Reaction score
1
:confused: :confused: :confused:
 
Physics news on Phys.org
The modulus of a real number is its absolute value. Since this is posted under quantum mechanics, I am assuming the the eigenvalue is real. In a more general case, though, the modulus of a complex number, a + bi, is \sqrt{a^2+b^2}.
 
Yes, if you regard a complex number as a vector in the plane (Feynmann;s "little arrows") then its modulus is its length. This obviously agrees with LeonhardEuler's algebraic definition.
 
I'd credit the arrows to Argand, not Feynman...
 
masudr said:
I'd credit the arrows to Argand, not Feynman...

Absolutely!:approve: I wasn't giving him credit for the idea, but in his little book QED he refers to the complex amplitudes on his paths as little arrows. I always thought that was both sharp and funny.
 
If u r talking of QM. Then this question appears meaningless to me.
In QM, every observable has got a hermitian operator representation. By the mathematics of hemitians we know they always have real eigenvalues.
so a mod amounts to change of sign if the eigval is -ve
 

Similar threads

Undergrad Meaning of eigenvalue of projection operator/projector
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad Commutators, operators and eigenvalues
  • · Replies 7 ·
Replies
7
Views
1K
Graduate Eigenvalue Problem of Quantum Mechanics
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Generalized Eigenvalues of Pauli Matrices
  • · Replies 1 ·
Replies
1
Views
1K
Graduate The eigenvalue power method for quantum problems
  • · Replies 2 ·
Replies
2
Views
2K
High School Correct English convention for |Psi|^2?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Velocity operator, its expression and eigenvalues
  • · Replies 27 ·
Replies
27
Views
4K
Undergrad Improper density matrix with negative eigenvalues
  • · Replies 27 ·
Replies
27
Views
4K
Graduate Changing Hamiltonian with some eigenvalues constant
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad It seems that the eigenvalue problem rules out the possibility of E=0?
  • · Replies 5 ·
Replies
5
Views
2K