A class of partially solvable two-dimensional quantum models with periodic potentials
نویسنده
چکیده
The supersymmetric approach is used to analyse a class of two-dimensional quantum systems with periodic potentials. In particular, the method of SUSY-separation of variables allowed us to find a part of the energy spectra and the corresponding wave functions (partial solvability) for several models. These models are not amenable to conventional separation of variables, and they can be considered as two-dimensional generalizations of Lamé, associated Lamé, and trigonometric Razavy potentials. All these models have the symmetry operators of fourth order in momenta, and one of them (the Lamé potential) obeys the property of self-isospectrality.
منابع مشابه
Periodic Potentials and Supersymmetry
We review the current status of one dimensional periodic potentials and also present several new results. It is shown that using the formalism of supersymmetric quantum mechanics, one can considerably enlarge the limited class of analytically solvable one-dimensional periodic potentials. Further, using the Landen transformations as well as cyclic identities for Jacobi elliptic functions discove...
متن کاملNew Solvable and Quasi Exactly Solvable Periodic Potentials
Using the formalism of supersymmetric quantum mechanics, we obtain a large number of new analytically solvable one-dimensional periodic potentials and study their properties. More specifically, the supersymmetric partners of the Lamé potentials ma(a+ 1) sn(x,m) are computed for integer values a = 1, 2, 3, .... For all cases (except a = 1), we show that the partner potential is distinctly differ...
متن کاملComment on “Self-Isospectral Periodic Potentials and Supersymmetric Quantum Mechanics”
We show that the formalism of supersymmetric quantum mechanics applied to the solvable elliptic function potentials V (x) = mj(j + 1)sn(x,m) produces new exactly solvable onedimensional periodic potentials. In a recent paper, Dunne and Feinberg [1] have systematically discussed various aspects of supersymmetric quantum mechanics (SUSYQM) as applied to periodic potentials. In particular, they de...
متن کاملSupersymmetry in Quantum Mechanics
An elementary introduction is given to the subject of Supersymmetry in Quantum Mechanics which can be understood and appreciated by any one who has taken a first course in quantum mechanics. We demonstrate with explicit examples that given a solvable problem in quantum mechanics with n bound states, one can construct new exactly solvable n Hamiltonians having n-1,n-2,...,0 bound states. The rel...
متن کاملQuantum current modeling in nano-transistors with a quantum dot
Carbon quantum dots (CQDs) serve as a new class of ‘zero dimensional’ nanomaterial’s in thecarbon class with sizes below 10 nm. As light emitting nanocrystals, QDs are assembled from semiconductormaterials, from the elements in the periodic groups of II-VI, III-V or IV-VI, mainly thanks to impacts of quantum confinement QDs have unique optical properties such as brighter, highly pho...
متن کامل