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

[zoltrix]

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 ?

 

[Keith_McClary]

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.

 

[atyy]

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.

 

[vanhees71]

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.