Abstract:
An algebraic apparatus based on increasing B+p and decreasing Bp operators (p=2,3,…,N) is developed to solve the one-dimensional model of N interacting particles studied
by Calogero [J. Math. Phys., 10, 2191, 2197 (1969)]. The determination of the wave functions
of the Schrödinger equation is then reduced to the operation of differentiation. Explicit
expressions are obtained for the operators Bp and B+p for p=2,3, and 4. All the wave functions
for the case of four particles can be found by means of these expressions. For an arbitrary
number of particles this then yields an expression for two new series of wave functions
that depend on three quantum numbers. The operators of higher order can be found by
the same method
Citation:
A. M. Perelomov, “Algebraic approach to the solution of a one-dimensional model of N interacting particles”, TMF, 6:3 (1971), 364–391; Theoret. and Math. Phys., 6:3 (1971), 285–282
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Kumar Abhinav, B. Chandrasekhar, Vivek M. Vyas, Prasanta K. Panigrahi, “Heisenberg symmetry and collective modes of one dimensional unitary correlated fermions”, Physics Letters A, 381:5 (2017), 457
E Bettelheim, “Integrable quantum hydrodynamics in two-dimensional phase space”, J. Phys. A: Math. Theor., 46:50 (2013), 505001
Shashi C. L. Srivastava, Sudhir R. Jain, “Random reverse-cyclic matrices and screened harmonic oscillator”, Phys. Rev. E, 85:4 (2012)
Vladimir A. Yurovsky, Maxim Olshanii, David S. Weiss, Advances In Atomic, Molecular, and Optical Physics, 55, 2008, 61
J F Cariñena, A M Perelomov, M F Rañada, “Isochronous classical systems and quantum systems with equally spaced spectra”, J. Phys.: Conf. Ser., 87 (2007), 012007
Ryu Sasaki, NATO Science Series, 201, Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete, 2006, 259
Patrick Desrosiers, Luc Lapointe, Pierre Mathieu, “Generalized Hermite polynomials in superspace as eigenfunctions of the supersymmetric rational CMS model”, Nuclear Physics B, 674:3 (2003), 615
R. Caseiro, J.-P. Françoise, R. Sasaki, “Quadratic algebra associated with rational Calogero-Moser models”, Journal of Mathematical Physics, 42:11 (2001), 5329
Alexander Turbiner, Calogero—Moser— Sutherland Models, 2000, 473
S P Khastgir, A J Pocklington, R Sasaki, “Quantum Calogero-Moser models: integrability for all root systems”, J. Phys. A: Math. Gen., 33:49 (2000), 9033
S Chaturvedi, V Gupta, “Identities involving elementary symmetric functions”, J. Phys. A: Math. Gen., 33:29 (2000), L251
N. Gurappa, Prasanta K. Panigrahi, “Equivalence of the Calogero-Sutherland model to free harmonic oscillators”, Phys. Rev. B, 59:4 (1999), R2490
S. E. Konstein, “Three-particle Calogero model: Supertraces and ideals on the observables algebra”, Theoret. and Math. Phys., 116:1 (1998), 836–845
N. GURAPPA, PRASANTA K. PANIGRAHI, V. SRINIVASAN, “DEGENERACY STRUCTURE OF THE CALOGERO–SUTHERLAND MODEL: AN ALGEBRAIC APPROACH”, Mod. Phys. Lett. A, 13:05 (1998), 339
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