Application of Finite Orthogonal Polynomials to the Thermal Functions of Harmonic Oscillators. I. Reduced Partition Function of Isotopic Molecules

摘要: The utility as well limitations of the Taylor series expansion quantum‐mechanical partition function a harmonic oscillator is discussed. Finite orthogonal polynomials are suggested basis for approximation thermodynamic functions an assumbly oscillators. Shifted Chebyshev first kind used to obtain finite expansions arbitrary order reduced isotopic molecules. resulting similar, except modulating coefficients, term by Bernoulli obtained from expansion. coefficients each in approach unity increases. Thus, developed here approaches asymptotically. converges much faster than radius convergence can be made arbitrarily large contrast limit 2π which exists expansion....