# Spin 0 boson interaction

I have a question regarding the interaction of two spin 0 bosons in a shared harmonic oscillator. What would their first excited state be?

I'm thinking that the total state has to be symmetric so the spatial part should to be symmetric. However, I'm confused about the spin state. Would it just be:

$$\mid{00}\rangle$$

and if so wouldn't the total state be just zero?

The spin of both components $$s_1=0$$, $$s_2=0$$, hence the total spin $$S= |s_1-s_2|, \dots s_1+s_2$$ can only be $$0$$. The spin part of the wavefunction is always going to be a singlet. The spatial part is the one that solely determines the energy.