We exhibit the solution of the initial-value problem for the system of 2N + 2 oscillators characterized by the Hamiltonian where N is an arbitrary positive integer, Ω, b and ωn 2 are N + 2 arbitrary real constants, q̂m, q̂m with m = 0,1,⋯,N are the 2N + 2 canonical coordinates and p̂m, p̌m the corresponding 2N + 2 canonical momenta. In the classical context the solution is completely periodic with period T = 2π/|Ω| (for arbitrary initial data). In the quantal context the (infinitely degenerate) spectrum is equispaced, with spacing ℏ|Ω|; all the corresponding eigenfunctions are also exhibited. This finding obtains as special case of a more general (new) class of isochronous Hamiltonians. © 2010 The Author(s).
Isochronous oscillators / Calogero, Francesco; F., Leyvraz. - In: JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS. - ISSN 1402-9251. - 17:1(2010), pp. 103-110. [10.1142/s1402925110000611]
Isochronous oscillators
CALOGERO, Francesco;
2010
Abstract
We exhibit the solution of the initial-value problem for the system of 2N + 2 oscillators characterized by the Hamiltonian where N is an arbitrary positive integer, Ω, b and ωn 2 are N + 2 arbitrary real constants, q̂m, q̂m with m = 0,1,⋯,N are the 2N + 2 canonical coordinates and p̂m, p̌m the corresponding 2N + 2 canonical momenta. In the classical context the solution is completely periodic with period T = 2π/|Ω| (for arbitrary initial data). In the quantal context the (infinitely degenerate) spectrum is equispaced, with spacing ℏ|Ω|; all the corresponding eigenfunctions are also exhibited. This finding obtains as special case of a more general (new) class of isochronous Hamiltonians. © 2010 The Author(s).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
