How are wavefunctions and eigenkets used differently in quantum mechanics?

  • Context: Graduate 
  • Thread starter Thread starter carllacan
  • Start date Start date
  • Tags Tags
    Wavefunctions
Click For Summary
SUMMARY

The discussion focuses on the differences between wavefunctions and eigenkets in quantum mechanics, highlighting the approaches of Griffiths and Sakurai. Wavefunctions are defined as coefficients in a state's expansion on the position basis, while eigenkets represent states in Hilbert space. The action of operators on wavefunctions produces new functions, exemplified by the momentum operator's effect on a wavefunction. The conversation emphasizes the importance of mathematical depth for understanding these concepts and recommends studying Ballentine's "Quantum Mechanics" and Sakurai's "Modern Quantum Mechanics" for a clearer grasp of the subject.

PREREQUISITES
  • Understanding of quantum mechanics fundamentals
  • Familiarity with Hilbert space concepts
  • Knowledge of operators in quantum mechanics
  • Basic grasp of Born's rule and probability distributions
NEXT STEPS
  • Study "Quantum Mechanics" by Ballentine for advanced concepts
  • Read "Modern Quantum Mechanics" by Sakurai for foundational understanding
  • Explore the mathematical framework of Hilbert spaces and operators
  • Investigate the implications of Gleason's theorem in quantum mechanics
USEFUL FOR

Students and professionals in physics, particularly those studying quantum mechanics, as well as educators seeking to clarify the distinctions between wavefunctions and eigenkets for their curriculum.

  • #31
micromass said:
Don't excuse yourself for asking. We are here to answer questions like yours!

But yes, ##\psi(x)## is a scalar, so you can treat it like one.

The wavefunction ##\psi## itself must be treated as a vector.

Thank you for your help!
 

Similar threads

Undergrad Are certain combinations of quantum numbers (basis vectors) forbidden?
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Magnetic field produced by moving charge in operator form
  • · Replies 14 ·
Replies
14
Views
2K
Undergrad Density Operators of Pure States
  • · Replies 21 ·
Replies
21
Views
3K
Graduate Is the wavefunction subjective? How?
  • · Replies 128 ·
5
Replies
128
Views
14K
Undergrad Understanding Operators in Matrix Mechanics
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Eigenvalue Problem of Quantum Mechanics
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Weakly interacting electrons in an atom
  • · Replies 2 ·
Replies
2
Views
2K
Graduate How Does the Wavefunction for n-Particles Relate to One-Dimensional Systems?
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad How to get the wavefunction of a single particle in QFT?
  • · Replies 2 ·
Replies
2
Views
2K
High School How to determine the wavefunction of photons?
  • · Replies 4 ·
Replies
4
Views
2K