Independent Eigenstates of Angular Momentum in a Quantum N-body System

The global rotational degrees of freedom in the Schr\"{o}dinger equation for an $N$-body system are completely separated from the internal ones. After removing the motion of center of mass, we find a complete set of $(2\ell+1)$ independent base functions with the angular momentum $\ell$. These are homogeneous polynomials in the components of the coordinate vectors and the solutions of the Laplace equation, where the Euler angles do not appear explicitly. Any function with given angular momentum and given parity in the system can be expanded with respect to the base functions, where the coefficients are the functions of the internal variables. With the right choice of the base functions and the internal variables, we explicitly establish the equations for those functions. Only (3N-6) internal variables are involved both in the functions and in the equations. The permutation symmetry of the wave functions for identical particles is discussed.Comment: 24 pages, no figure, one Table, RevTex, Will be published in Phys. Rev. A 64, 0421xx (Oct. 2001

Thyroid control over biomembranes: VI. Lipids in liver mitochondria and microsomes of hypothyroid rats

The lipids of liver mitochondria prepared from normal rats and from rats made hypothyroid by thyroidectomy and injection with131INa contained similar amounts, per mg protein, of total lipids, phospholipids, neutral lipids and lipid phosphorus. Hypothyroidism caused a doubling of the relative amounts of mitochondrial cardiolipins (CL; to 20.5% of the phospholipid P) and an accompanying trend (although statistically not significant) toward decreased amounts of both phosphatidylcholines (PC) and phosphatidylserines (PS), with phosphatidylethanolamines (PE) remaining unchanged. The pattern of elevated 18∶2 fatty acyl content and depleted 20∶4 acyl groups of the mitochondrial phospholipids of hypothyroid preparations was reflected to varying degrees in the resolved phospholipids, with PC showing greater degrees of abnormality than PE, and CL showing none. Hypothyroidism produced the same abnormal pattern of fatty acyl distributions in liver microsomal total lipids as was found in the mitochondria. Hypothyroid rats, when killed 6 hr after injection of [1‐14C] labeled linoleate, showed the following abnormalities: the liver incorporated less label into lipids, and converted 18∶2 not exclusively to 20∶4 (as normals do) but instead incorporated the label mainly into saturated fatty acids. These data, together with the known decrease in β‐oxidation, suggest that hypothyroidism involves possible defective step(s) in the conversion of 18∶2 to 20∶4.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142296/1/lipd0328.pd