The Linear Potential Propagator via Wave Function Expansion

ABSTRACT: We evaluate the quantum propagator for the motion of a particle in a linear potential via a recently developped formalism [A.B. Nassar et al., Phys. Rev. E56, 1230, (1997)]. In this formalism, the propagator comes about as a type of expansion of the wave function over the space of the initial velocities.

GABA and glutamate transporters: new events and function in the vertebrate retina

The neural retina is a highly complex tissue composed of excitatory and inhibitory neurons and glial cells. Glutamate, the main excitatory neurotransmitter, mediates information transfer from photoreceptors, bipolar cells, and ganglion cells, whereas interneurons, mainly amacrine and horizontal cells, use γ-aminobutyric acid (GABA), the main inhibitory neurotransmitter. In this review we place an emphasis on glutamate and GABA transporters as highly regulated molecules that play fundamental roles in neurotransmitter clearance, neurotransmitter release, and oxidative stress. We pharmacologically characterized glutamate transporters in chicken retina cells and identified two glutamate transporters: one Na+-dependent transporter and one Na+-independent transporter. The Na+-dependent uptake system presented characteristics related to the high-affinity xAG- system (EAAT1), and the Na+-independent uptake system presented characteristics related to the xCG- system, which highly contributes to glutamate transport in the retina. Glutamate shares the xCG- system with another amino acid, L-cysteine, suggesting the possible involvement of glutathione. Both transporter proteins are present mainly in Müller glial cells. GABA transporters (GATs) mediate high-affinity GABA uptake from the extracellular space and terminate the synaptic action of GABA in the central nervous system. GABA transporters can be modulated by molecules that act on specific sites to promote transporter phosphorylation and dephosphorylation. In addition to a role in the clearance of GABA, GATs may also release GABA through a reverse transport mechanism. In the chicken retina, a GAT-1 blocker, but not GAT2/3 blocker, was shown to inhibit GABA uptake, suggesting that GABA release from retina cells is mainly mediated by a GAT-1-like transporter.