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The Schr\"odinger integral-equation approach for calculating the classicalfirst-passage time (C-fpt) probability density is extended to the case ofquantum first-passage time (Q-fpt). Using this extension, we have calculatedanalytically the Q-fpt probability density for a class of few-site/statetight-binding Hamiltonian systems, e.g., a qubit, as well as for an infinite 1Dlattice. The defining feature of such a quantum system is that the passageacross the boundary between a subspace (omega) and its complement (omega-bar)is through a unique pair of "door-way" sites such that the first departure from(arrival at) omega corresponds to the first arrival at (departure from)omega-bar. The Q-fpt probability density so derived remains positive over thetime interval in which it also normalizes to unity. These conditions ofpositivity and normalization define the physical time domain for the Q-fptproblem. This time domain is found to remain finite for the few-site/stateHamiltonian systems considered here, which is quite unlike the case for thediffusive C-fpt problems. The door-way sites and the associated Q-fptprobability density derived here should be relevant tointer-biomolecular/nanostructural electron transport phenomena.

Quantum First-Passage Time: Exact Solutions for a Class of Tight-Binding Hamiltonian Systems