منابع مشابه
Equilibrium Positions and Eigenfunctions of Shape Invariant (‘Discrete’) Quantum Mechanics
Certain aspects of the integrability/solvability of the Calogero-Sutherland-Moser systems and the Ruijsenaars-Schneider-van Diejen systems with rational and trigonometric potentials are reviewed. The equilibrium positions of classical multi-particle systems and the eigenfunctions of single-particle quantum mechanics are described by the same orthogonal polynomials: the Hermite, Laguerre, Jacobi...
متن کاملEquilibrium Positions, Shape Invariance and Askey-Wilson Polynomials
We show that the equilibrium positions of the Ruijsenaars-Schneider-van Diejen systems with the trigonometric potential are given by the zeros of the Askey-Wilson polynomials with five parameters. The corresponding single particle quantum version, which is a typical example of “discrete” quantum mechanical systems with a q-shift type kinetic term, is shape invariant and the eigenfunctions are t...
متن کاملPolynomials Associated with Equilibrium Positions in Calogero-Moser Systems
In a previous paper (Corrigan-Sasaki), many remarkable properties of classical Calogero and Sutherland systems at equilibrium are reported. For example, the minimum energies, frequencies of small oscillations and the eigenvalues of Lax pair matrices at equilibrium are all “integer valued”. The equilibrium positions of Calogero and Sutherland systems for the classical root systems (Ar, Br, Cr an...
متن کاملAffective and metabolic responses to hypnosis, autogenic relaxation, and quiet rest in the supine and seated positions.
This study examined the influence of hypnosis, autogenic relaxation, and quiet rest on selected affective states and metabolism. The influence of body position (seated vs. supine) on these same outcome measures was also investigated. Anxiety, tension, and overall mood were assessed before and 30 minutes after each treatment, and oxygen uptake was measured continuously. State anxiety, tension, a...
متن کاملThe effects of finger rest positions on hand muscle load and pinch force in simulated dental hygiene work.
One of the techniques taught in dental and dental hygiene programs is to use finger rests to stabilize the instrument while performing dental scaling or other types of dental work. It is believed that finger rests may also reduce muscle stress and prevent injury due to muscle fatigue. In this study the effects of three different finger rest positions on hand muscle activity and thumb pinch forc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Scientific American
سال: 1911
ISSN: 0036-8733
DOI: 10.1038/scientificamerican01281911-88