This paper investigates the unique continuation properties of solutions of the electromagnetic Schr\"{ o}dinger equation $$ i\partial_{ t}u(x,t)+(\nabla-i A)^{ 2}u(x,t)=V(x,t)u(x,t)\,\,\,\, \mbox{ in} \,\,\,\mathbb{ R}^{ n}\times [0,1], $$ where $A$ represents a time-independent magnetic vector potential and $V$ is a bounded, complex valued time-dependent potential. Given $1<p<2$ and $1/p+1/q=1$, we prove that if \begin{ equation*} \int_{ \mathbb{ R}^{ n}}|u(x,0)|^{ 2}e^{ 2\alpha^{ p}|x|^p/p}\ d x +\int_{ \mathbb{ R}^{ n}}|u(x,1)|^{ 2}e^{ 2\beta^{ q}|x|^q/q}\ d x <\infty, \end{ equation*} for some $\alpha,\beta>0$ and there exists $N_{ p}>0$ such that \begin{ equation*} \alpha\beta>N_p, \end{ equation*} then $u\equiv 0$. These results can be interpreted as dynamical versions of the uncertainty principle of Morgan's type. Furthermore, as an application, our results extend to a large class of semi-linear Schr\"{ o}dinger equations.
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