Imaginary part of the wave function about qmsolve HOT 3 OPEN

Hi,

The harmonic oscillator and any other system subjected to a real value potential V(x) only have real-valued eigenstates up to an arbitrary complex constant with a module equal to 1.

Eigenstates of the 1D harmonic oscillator are:

Which they are normalized in such a way that they only have a real part.

from qmsolve.

Yes but the 3D harmonic oscillator has the spherical harmonics function :

from qmsolve.

The complex spherical harmonic basis is not the unique basis of the 3D harmonic oscillator due to energy degeneracy. This solver will normally converge separately to the real $\frac{Y^{m}_l + Y^{-m}_l}{2}$ and imaginary part $\frac{Y^{m}_l - Y^{-m}_l}{2i}$ of the wavefunction you cite, which form a basis with the same span as the m = +-1 spherical harmonics $Y^{m}_l$ and $Y^{-m}_l$

For the hydrogen atom, it will happen exactly the same: instead of converging to the complex spherical harmonics, it will converge to the basis it's usually used in chemistry books to represent p orbitals. However, if you turn on a magnetic field, as illustrated in the Zeeman effect example, the degeneracy breaks and the eigenstates will converge to wavefunctions with the angular part approaching the complex spherical harmonics.

from qmsolve.