  The time-energy uncertainty relation in nonrelativistic quantum mechanics has
been intensely debated with regard to its formal derivation, validity, and
physical meaning. Here, we analyze two formal relations proposed by Mandelstam
and Tamm and by Margolus and Levitin and evaluate their validity using a
minimal quantum toy model composed of a single qubit inside an external
magnetic field. We show that the $\ell_1$ norm of energy coherence
$\mathcal{C}$ is invariant with respect to the unitary evolution of the quantum
state. Thus, the $\ell_1$ norm of energy coherence $\mathcal{C}$ of an initial
quantum state is useful for the classification of the ability of quantum
observables to change in time or the ability of the quantum state to evolve
into an orthogonal state. In the single-qubit toy model, for quantum states
with the submaximal $\ell_1$ norm of energy coherence, $\mathcal{C}<1$, the
Mandelstam-Tamm and Margolus-Levitin relations generate instances of infinite
"time uncertainty" that is devoid of physical meaning. Only for quantum states
with the maximal $\ell_1$ norm of energy coherence, $\mathcal{C}=1$, the
Mandelstam-Tamm and Margolus-Levitin relations avoid infinite "time
uncertainty", but they both reduce to a strict equality that expresses the
Einstein-Planck relation between energy and frequency. The presented results
elucidate the fact that the time in the Schr\"{o}dinger equation is a scalar
variable that commutes with the quantum Hamiltonian and is not subject to
statistical variance.
