Physics – Mathematical Physics
Scientific paper
2009-02-13
J. Phys. A: Math. Theor. 42 (2009) 125301 (16pp)
Physics
Mathematical Physics
Scientific paper
10.1088/1751-8113/42/12/125301
We consider quantum systems consisting of a linear chain of n harmonic oscillators coupled by a nearest neighbour interaction of the form $-q_r q_{r+1}$ ($q_r$ refers to the position of the $r$th oscillator). In principle, such systems are always numerically solvable and involve the eigenvalues of the interaction matrix. In this paper, we investigate when such a system is analytically solvable, i.e. when the eigenvalues and eigenvectors of the interaction matrix have analytically closed expressions. This is the case when the interaction matrix coincides with the Jacobi matrix of a system of discrete orthogonal polynomials. Our study of possible systems leads to three new analytically solvable Hamiltonians: with a Krawtchouk interaction, a Hahn interaction or a q-Krawtchouk interaction. For each of these cases, we give the spectrum of the Hamiltonian (in analytic form) and discuss some typical properties of the spectra.
der Jeugt Joris Van
Regniers Gilles
No associations
LandOfFree
Analytically solvable Hamiltonians for quantum systems with a nearest neighbour interaction does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Analytically solvable Hamiltonians for quantum systems with a nearest neighbour interaction, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Analytically solvable Hamiltonians for quantum systems with a nearest neighbour interaction will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-357379