aqora

Exact Solutions of the Schrödinger Equation with Position-dependent Effective Mass via General Point Canonical Transformation

C. Tezcan, R. Sever

Journal of Mathematical ChemistryJun 12, 200649 citations

Equivalence of Momentum Operators in Generalized Coordinates

Gary R. Gruber

American Journal of PhysicsNov 1, 19723 citations

Isospectral Hamiltonian for position-dependent mass for an arbitrary quantum system and coherent states

Sid-Ahmed Yahiaoui, M. Bentaïba

By means of the unitary transformation, a new way for discussing the ordering prescription of the Schrödinger equation with a position-dependent mass (PDM) for isospectral Hamiltonian operators is presented. We show that the ambiguity parameter choices in the kinetic part of the Hamiltonian can be explained through an exact SUSY QM symmetry as well as a consequence of an accidental symmetry under the Z2 action. By making use of the unitary transformation, we construct coherent states for a family of PDM isospectral Hamiltonians from a suitable choice of ladder operators. We show that these states preserve the usual structure of Klauder-Perelomov’s states and thus saturate and minimize the position-momentum uncertainty relation (PMUR) under some special restrictions. We show that PMUR properties can be used to determine the sign of the superpotential.By means of the unitary transformation, a new way for discussing the ordering prescription of the Schrödinger equation with a position-dependent mass (PDM) for isospectral Hamiltonian operators is presented. We show that the ambiguity parameter choices in the kinetic part of the Hamiltonian can be explained through an exact SUSY QM symmetry as well as a consequence of an accidental symmetry under the Z2 action. By making use of the unitary transformation, we construct coherent states for a family of PDM isospectral Hamiltonians from a suitable choice of ladder operators. We show that these states preserve the usual structure of Klauder-Perelomov’s states and thus saturate and minimize the position-momentum uncertainty relation (PMUR) under some special restrictions. We show that PMUR properties can be used to determine the sign of the superpotential.

arXiv:1611.05394Journal of Mathematical PhysicsJun 1, 20178 citations

Momentum and Hamiltonian operators in generalized coordinates

Makoto Kato

International Journal of Theoretical PhysicsApr 1, 19940 citations

Position‐dependent mass Schrödinger equations allowing harmonic oscillator (HO) eigenvalues

José Juan Peña, Gerardo Ovando, J. Morales +2 more

Abstract Quantum chemical systems with a position‐dependent mass have attracted the attention due to their relevance in describing the features of many microstructures of current interest. In this work, the point canonical transformation method applied to Schrödinger equations with a position‐dependent mass (SEPDM) is presented. Essentially, the proposal is aimed to transform the Schrödinger equation with a position‐dependent mass into a standard Schrödinger‐like equation for constant mass in such a way that the position‐dependent mass distribution (PDMD) becomes incorporated into the effective potential. As an useful application of the proposal, it is considered as effective potential the one‐dimensional harmonic oscillator potential model, which leads to those isospectral potentials related to different forms of PDMD. For example, the exactly solvable isospectral potentials involved in the SEPDM for some PDMD such as , , , , , xα, and , are worked out explicitly including their raising and lowering operators that factorize the SEPDM for each PDMD allowing HO eigenvalues. However, the proposal is general and can be straightforwardly applied to other effective potential models as well as other PDMD that could be useful in quantum chemical applications. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008Abstract Quantum chemical systems with a position‐dependent mass have attracted the attention due to their relevance in describing the features of many microstructures of current interest. In this work, the point canonical transformation method applied to Schrödinger equations with a position‐dependent mass (SEPDM) is presented. Essentially, the proposal is aimed to transform the Schrödinger equation with a position‐dependent mass into a standard Schrödinger‐like equation for constant mass in such a way that the position‐dependent mass distribution (PDMD) becomes incorporated into the effective potential. As an useful application of the proposal, it is considered as effective potential the one‐dimensional harmonic oscillator potential model, which leads to those isospectral potentials related to different forms of PDMD. For example, the exactly solvable isospectral potentials involved in the SEPDM for some PDMD such as , , , , , xα, and , are worked out explicitly including their raising and lowering operators that factorize the SEPDM for each PDMD allowing HO eigenvalues. However, the proposal is general and can be straightforwardly applied to other effective potential models as well as other PDMD that could be useful in quantum chemical applications. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

International Journal of Quantum ChemistryJan 1, 20085 citations

Schrödinger Equation with Position-Dependent Mass

Shi‐Hai Dong

Springer eBooksJan 1, 20110 citations

Position-dependent mass momentum operator and minimal coupling: point canonical transformation and isospectrality

Related papers

Position-dependent mass momentum operator and minimal coupling: point canonical transformation and isospectrality

Related papers