QHO Solutions: What is Imaginary Part?

[LarryS]

The solutions, in the position basis, of the Schrödinger Equation for the Quantum Harmonic Oscillator are a family of functions based on the Hermite Polynomials. The Wikipedia link for this subject is http://en.wikipedia.org/wiki/Quantum_harmonic_oscillator .

But this Wikipedia article and most of what I have read on this topic only descirbes the REAL part of this family of solutions. What is, or where can I read about, the IMAGINARY part of these wave functions?

As always, thanks in advance.

 

[psmt]

There is a theorem (see Sakurai and Napolitano, Modern QM, Second Edition) that for a time-reversal-independent Hamiltonian (such as the one under consideration here), non-denegerate energy eigenfunctions of a spinless particle can always be chosen to be real. Then choosing them to be purely real, rather than having a global phase factor, is merely an extremely sensible convention.