1,2

The asymptotic eigenvalue spectrum of the Schroedinger equation for a free particle in a box in three dimensions is known only (that is: average level density and average degeneracy) if the a(n) are finite series.

H.-P. Baltes, Peter K. J. Draxl and Eberhard R. Hilf, Quadratsummen und gewisse Randwertprobleme der Mathematischen Physik, Journ. Reine Angewandte Mathematik, Vol. 268/269, 1974, 410-417.

E. Grosswald, A. Calloway and J. Calloway, The representations of integers by three positive squares, Proc. Amer. Math. Soc. 10 (1959), 451-455. [Math. Rev. 21 #3376; E24-73 in Leveque's Reviews in Number Theory, Vol. 2, p. 290]

E. R. Hilf, Diploma-thesis, Univ.Frankfurt,Germany, 1963 [available from author]

E. R. Hilf, G. Suessmann, Surface Tension of nuclei according to the Fermigas-Model; Physics Letters, Vol. 21, No. 6, p. 654-656, (1966)

H. P. Baltes and E. R. Hilf, Spectra of finite systems; BI-Verlag

Eberhard R. Hilf, Publications

E. R. Hilf and H. P. Baltes, 130 and the cube spectrum, unpublished

Index entries for sequences related to sums of squares

Consider a(3)=5: 1^2 +1^2 +1^2=3, too low; 1^2+1^2+2^2=6, too high. 4^1=4 too low; 4^2=16 too high; (8*0+7)=7 too low, (8*1+7)= 15 too high; thus 5 is a member of this sequence.

Sequence in context: A135467 A018571 A064233 this_sequence A103188 A064392 A018296

Adjacent sequences: A051949 A051950 A051951 this_sequence A051953 A051954 A051955

hard,nonn,nice

Eberhard R. Hilf (hilf(AT)merlin.physik.uni-oldenburg.de), Dec 21 1999

It is not known whether 130 is the largest such number or if this is the start of an infinite series.

Grosswald et al. reference from N. J. A. Sloane (njas(AT)research.att.com), Jun 07 2000.