Calculation of Band Edge Eigenfunctions and Eigenvalues of Periodic Potentials through the Quantum Hamilton - Jacobi Formalism

We obtain the band edge eigenfunctions and the eigenvalues of solvable periodic potentials using the quantum Hamilton - Jacobi formalism. The potentials studied here are the Lam{\'e} and the associated Lam{\'e} which belong to the class of elliptic potentials. The formalism requires an assumption about the singularity structure of the quantum momentum function $p$, which satisfies the Riccati type quantum Hamilton - Jacobi equation, $p^{2} -i \hbar \frac{d}{dx}p = 2m(E- V(x))$ in the complex $x$ plane. Essential use is made of suitable conformal transformations, which leads to the eigenvalues and the eigenfunctions corresponding to the band edges in a simple and straightforward manner. Our study reveals interesting features about the singularity structure of $p$, responsible in yielding the band edge eigenfunctions and eigenvalues.Comment: 21 pages, 5 table

Disruption of a structurally important extracellular element in the Glycine Receptor leads to decreased synaptic integration and signaling resulting in Severe Startle Disease

Functional impairments or trafficking defects of inhibitory glycine receptors (GlyRs) have been linked to human hyperekplexia/startle disease and autism spectrum disorders. We found that a lack of synaptic integration of GlyRs, together with disrupted receptor function, is responsible for a lethal startle phenotype in a novel spontaneous mouse mutant shaky, caused by a missense mutation, Q177K, located in the extracellular β8–β9 loop of the GlyR α1 subunit. Recently, structural data provided evidence that the flexibility of the β8–β9 loop is crucial for conformational transitions during opening and closing of the ion channel and represents a novel allosteric binding site in Cys-loop receptors. We identified the underlying neuropathological mechanisms in male and female shaky mice through a combination of protein biochemistry, immunocytochemistry, and both in vivo and in vitro electrophysiology. Increased expression of the mutant GlyR α1Q177K subunit in vivo was not sufficient to compensate for a decrease in synaptic integration of α1Q177Kβ GlyRs. The remaining synaptic heteromeric α1Q177Kβ GlyRs had decreased current amplitudes with significantly faster decay times. This functional disruption reveals an important role for the GlyR α1 subunit β8–β9 loop in initiating rearrangements within the extracellular–transmembrane GlyR interface and that this structural element is vital for inhibitory GlyR function, signaling, and synaptic clustering

Accuracy of Semiclassical Methods for Shape Invariant Potentials

We study the accuracy of several alternative semiclassical methods by computing analytically the energy levels for many large classes of exactly solvable shape invariant potentials. For these potentials, the ground state energies computed via the WKB method typically deviate from the exact results by about 10%, a recently suggested modification using nonintegral Maslov indices is substantially better, and the supersymmetric WKB quantization method gives exact answers for all energy levels.Comment: 7 pages, Latex, and two tables in postscrip

Spinal Cord Infarction with Multiple Etiologic Factors

Spinal cord infarction is uncommon and usually presents with sudden onset of paralysis and sensory disturbances. A variety of causes are described, but rarely with multiple factors involved. We report a case of a 63-year-old man with a history of diabetes mellitus, hypertension, and osteoarthritis who presented with acute onset of chest pain, numbness, and weakness associated with episodic hypotension. He had incomplete tetraplegia and was areflexic without spasticity. Pain and temperature sensations were impaired below the C7 dermatome and absent below the T4 dermatome bilaterally. Proprioception and vibration sensations were diminished on the right below the C6 dermatome. Magnetic resonance imaging showed spinal cord infarction affecting C6–T3 segments, and severe cervical and lumbar spine degenerative changes. This case illustrates an unusual presenting symptom of spinal infarction, the need to identify multiple risk factors for spinal cord infarction, and the importance of optimal preventive therapy in patients at risk

Measurement of the Neutron Radius of 208Pb Through Parity-Violation in Electron Scattering

We report the first measurement of the parity-violating asymmetry A_PV in the elastic scattering of polarized electrons from 208Pb. A_PV is sensitive to the radius of the neutron distribution (Rn). The result A_PV = 0.656 \pm 0.060 (stat) \pm 0.014 (syst) ppm corresponds to a difference between the radii of the neutron and proton distributions Rn - Rp = 0.33 +0.16 -0.18 fm and provides the first electroweak observation of the neutron skin which is expected in a heavy, neutron-rich nucleus.Comment: 6 pages, 1 figur