Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension

Journal of Mathematical Physics - Tập 1 Số 6 - Trang 516-523 - 1960
M. D. Girardeau1
1Brandeis University, Waltham, Massachusetts

Tóm tắt

A rigorous one-one correspondence is established between one-dimensional systems of bosons and of spinless fermions. This correspondence holds irrespective of the nature of the interparticle interactions, subject only to the restriction that the interaction have an impenetrable core. It is shown that the Bose and Fermi eigenfunctions are related by ψB=ψFA, where A(x1 … xn) is +1 or −1 according as the order pq … r, when the particle coordinates xj are arranged in the order xp<xq< … <xr, is an even or an odd permutation of 1 … n. The energy spectra of the two systems are identical, as are all configurational probability distributions, but the momentum distributions are quite different. The general theory is illustrated by application to the special case of impenetrable point particles; the one-one correspondence between bosons with this particular interaction and completely noninteracting fermions leads to a rigorous solution of this many-boson problem.

Từ khóa


Tài liệu tham khảo

1956, Phys. Rev., 104, 576, 10.1103/PhysRev.104.576

1955, J. Chem. Phys., 23, 1183, 10.1063/1.1742236

1960, Bull. Am. Phys. Soc. Ser. II, 5, 8

1942, Phys. Rev., 61, 524, 10.1103/PhysRev.61.524

1959, Phys. Rev., 116, 1057, 10.1103/PhysRev.116.1057

1947, J. Phys. (U.S.S.R.), 11, 23

1959, Phys. Rev., 113, 755, 10.1103/PhysRev.113.755

Thông tin
Thông tin xuất bản

Journal of Mathematical Physics

Tập 1 Số 6

516-523

Thông tin tác giả