Coherent states for Hamiltonians generated by supersymmetry

Abstract

Coherent states are derived for one-dimensional systems generated by supersymmetry from an initial Hamiltonian with a purely discrete spectrum for which the levels depend analytically on their subindex. It is shown that the algebra of the initial system is inherited by its SUSY partners in the subspace associated to the isospectral part or the spectrum. The technique is applied to the harmonic oscillator, infinite well and trigonometric Pöschl-Teller potentials.

Coherent states approach to Penning trap

“…Notice that |n 1 , n 2 , n 3 is eigenstate of the Penning trap Hamiltonian with eigenvalue E n 1 ,n 2 ,n 3 = ω 1 (n 1 + 1/2) − ω 2 (n 2 + 1/2) + ω 3 (n 3 + 1/2) ≡ E(n 1 , n 2 , n 3 ). In particular, the extremal state |0, 0, 0 has eigenvalue E 0,0,0 = (ω 1 − ω 2 + ω 3 )/2, i.e., it is neither a ground nor a top state since its energy is "in the middle" of the spectrum of H. Following [15], it is seen that there is an intrinsic algebraic structure for our system, which is characterized by a linear relationship between the Penning trap Hamiltonian H and the three number operators N k :…”

New coherent states with Laguerre polynomials coefficients for the symmetric Pöschl–Teller oscillator

“…Another interesting aspect of this potential lies in the fact that it has a quadratic spectrum leading to a rich revival structure for its coherent states, which makes possible the formation of Schrödinger cat and cat-like states. Different types of coherent states for quantum mechanical systems evolving in the PT potential have been discussed by many authors from different perspectives [4][5][6][7][8][9][10][11][12][13].…”

Rosen–Morse Potential and Its Supersymmetric Partners

“…SUSY techniques have been applied successfully to several one-dimensional Hamiltonians, e.g., the harmonic oscillator, infinite well and Pöschl-Teller potentials (trigonometric or hyperbolic) [6,[11][12][13][14][15][16][17]. For these systems the generic discrete energy level E n is a secondorder polynomial of the index n. This implies that there is an intrinsic algebraic structure (IAS) of Lie type involving the number, annihilation and creation operators, since the commutator between the ladder operators, which coincides with E n+1 − E n , is linear in n [16].…”

“…For these systems the generic discrete energy level E n is a secondorder polynomial of the index n. This implies that there is an intrinsic algebraic structure (IAS) of Lie type involving the number, annihilation and creation operators, since the commutator between the ladder operators, which coincides with E n+1 − E n , is linear in n [16]. It is important to study potentials with a different dependence for E n , such that the IAS is not longer of Lie type.…”