𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Group Theoretical Approach to the Intertwined Hamiltonians

✍ Scribed by José F. Cariñena; Arturo Ramos; David J. Fernández C.

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
143 KB
Volume
292
Category
Article
ISSN
0003-4916

No coin nor oath required. For personal study only.

✦ Synopsis

We show that the finite difference Bäcklund formula for the Schrödinger Hamiltonians is a particular element of the transformation group on the set of Riccati equations considered by two of us in a previous paper. Then, we give a group theoretical explanation to the problem of Hamiltonians related by a first order differential operator. A generalization of the finite difference algorithm relating eigenfunctions of three different Hamiltonians is found, and some illustrative examples of the theory are analyzed, finding new potentials for which one eigenfunction and its corresponding eigenvalue is exactly known.

📜 SIMILAR VOLUMES

A Group-Theoretical Approach to Quantum
A Group-Theoretical Approach to Quantum Optics || Index
✍ Klimov, Andrei B.; Chumakov, Sergei M. 📂 Article 📅 2009 🏛 Wiley-VCH Verlag GmbH & Co. KGaA 🌐 German ⚖ 31 KB 👁 3 views

Atomic Kinematics -- Atomic Dynamics -- Quantized Electromagnetic Field -- Field Dynamics -- The Jaynes-cummings Model -- Collective Interactions -- Atomic Systems In A Strong Quantum Field -- Quantum Systems Beyond The Rotating Wave Approximation -- Models With Dissipation -- Quasi-distributions In

A Group-Theoretical Approach to Quantum
A Group-Theoretical Approach to Quantum Optics || References
✍ Klimov, Andrei B.; Chumakov, Sergei M. 📂 Article 📅 2009 🏛 Wiley-VCH Verlag GmbH & Co. KGaA 🌐 German ⚖ 62 KB 👁 3 views

Atomic Kinematics -- Atomic Dynamics -- Quantized Electromagnetic Field -- Field Dynamics -- The Jaynes-cummings Model -- Collective Interactions -- Atomic Systems In A Strong Quantum Field -- Quantum Systems Beyond The Rotating Wave Approximation -- Models With Dissipation -- Quasi-distributions In

A Group-Theoretical Approach to Quantum
A Group-Theoretical Approach to Quantum Optics || Appendices
✍ Klimov, Andrei B.; Chumakov, Sergei M. 📂 Article 📅 2009 🏛 Wiley-VCH Verlag GmbH & Co. KGaA 🌐 German ⚖ 271 KB 👁 3 views

Atomic Kinematics -- Atomic Dynamics -- Quantized Electromagnetic Field -- Field Dynamics -- The Jaynes-cummings Model -- Collective Interactions -- Atomic Systems In A Strong Quantum Field -- Quantum Systems Beyond The Rotating Wave Approximation -- Models With Dissipation -- Quasi-distributions In

A Group-Theoretical Approach to Quantum
A Group-Theoretical Approach to Quantum Optics || Front Matter
✍ Klimov, Andrei B.; Chumakov, Sergei M. 📂 Article 📅 2009 🏛 Wiley-VCH Verlag GmbH & Co. KGaA 🌐 German ⚖ 81 KB 👁 2 views

Atomic Kinematics -- Atomic Dynamics -- Quantized Electromagnetic Field -- Field Dynamics -- The Jaynes-cummings Model -- Collective Interactions -- Atomic Systems In A Strong Quantum Field -- Quantum Systems Beyond The Rotating Wave Approximation -- Models With Dissipation -- Quasi-distributions In

A Group-Theoretical Approach to Quantum
A Group-Theoretical Approach to Quantum Optics || Atomic Kinematics
✍ Klimov, Andrei B.; Chumakov, Sergei M. 📂 Article 📅 2009 🏛 Wiley-VCH Verlag GmbH & Co. KGaA 🌐 German ⚖ 190 KB 👁 2 views

Atomic Kinematics -- Atomic Dynamics -- Quantized Electromagnetic Field -- Field Dynamics -- The Jaynes-cummings Model -- Collective Interactions -- Atomic Systems In A Strong Quantum Field -- Quantum Systems Beyond The Rotating Wave Approximation -- Models With Dissipation -- Quasi-distributions In