Which one is correct? (the Matrix or Wave formulation of QM)

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Discussion Overview

The discussion revolves around the equivalence of the matrix and wave formulations of quantum mechanics (QM), exploring their applications and preferences among professional scientists in solving real problems.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants assert that the matrix and wave formulations of QM are equivalent theories that yield the same results.
  • One participant mentions that certain systems can be treated as perturbations of the harmonic oscillator, suggesting that using the discrete harmonic oscillator basis can be computationally efficient.
  • Another participant describes the matrix formulation as being based on energy eigenvectors and eigenstates, emphasizing that both formulations are identical and that the distinction is more historical than practical.
  • A later reply argues that Dirac's formulation is clearer as it presents quantum theory in a "representation free" manner, indicating that the choice between wave mechanics and matrix mechanics depends on the specific problem being addressed.

Areas of Agreement / Disagreement

Participants express differing views on the practicality and clarity of the matrix versus wave formulations, indicating that while some see them as equivalent, others highlight the contextual preference based on specific problems.

Contextual Notes

The discussion does not resolve the nuances of when one formulation may be preferred over the other, nor does it clarify the implications of using different bases in quantum mechanics.

zoltrix
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hello

matrix and wave formulation of QM are equivalent theories i.e they yield the same results
Which one is most frequentely used by professional scientists in solving real problems and why ?
 
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For example, some systems can be considered perturbations of the harmonic oscillator, so it is computationally efficient to work in the discrete harmonic oscillator basis.
 
Roughly, the matrix version is the formulation in terms of energy eigenvectors and eigenstates. The two formulations are identical, so in practice one goes seamlessly between the two fomulations. One doesn't think of them as separate formulations nowadays, as thinking of them as separate formulations is more confusing and historical than helpful. They are the same formulation.
 
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That's why Dirac's formulation after all is the most clear formulation, because it is formulating QT in a "representation free" way. Then whether you do "wave mechanics" or "matrix mechanics" is simply the same theory using different bases to solve some problem, and which one is more convenient depends on the problem you want to solve.
 
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