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In this paper, we prove restriction theorems for the Fourier-Laguerretransform and establish Strichartz estimates for the Schr\"{o}dinger propagator$e^{-itL_\alpha}$ for the Laguerre operator$L_\alpha=-\Delta-\sum_{j=1}^{n}(\dfrac{2\alpha_j+1}{x_j}\dfrac{\partial}{\partialx_j})+\dfrac{|x|^2}{4}$,$\alpha=(\alpha_1,\alpha_2,\cdots,\alpha_n)\in{(-\frac{1}{2},\infty)^n}$ on$\mathbb{R}_+^n$ involving systems of orthonormal functions.

Restriction theorems and Strichartz inequalities for the Laguerre operator involving orthonormal functions