I have this question,when i was told QM they taught me some axioms:(1D)(adsbygoogle = window.adsbygoogle || []).push({});

The wave function of the particle is given by the differential equation:

[tex]i\hbar\frac{d\psi}{dt}=\frac{-\hbar^{2}}{2m}D^{2}\psi+V(x)\psi [/tex] with D=d/dx

and that the eigenfunctions of [tex]H\phi=E_{n}\phi[/tex] are all orthogonal and are on L^2(R) function space....

i have discussed in other forum a method to obtain RH by assuming that a Hamiltonian have its energies being the eigenvalues of a certain function f(x) my question in this case is if:

a)does the Schroedinguer equation have always a solution independent of what the potential V is?.,let,s suppose that potential is dicontinous everywhere (impossible but mathematically true).

b)are always the eigenfnction of the Hamiltonian on the space L^2(R)

c)can we always say that exist a potential V so the energies of the system are the roots of a certain function f(x)?...

i have some discussion with mathematicians there saying that ...

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# QM axioms¿always true?

**Physics Forums | Science Articles, Homework Help, Discussion**