Hidden symmetries in one-dimensional quantum Hamiltonians
نویسنده
چکیده
We construct a Heisenberg-like algebra for the one dimensional infinite square-well potential in quantum mechanics. The numbertype and ladder operators are realized in terms of physical operators of the system as in the harmonic oscillator algebra. These physical operators are obtained with the help of variables used in a recently developed non commutative differential calculus. This “square-well algebra” is an example of an algebra in a large class of generalized Heisenberg algebras recently constructed. This class of algebras also contains q-oscillators as a particular case. We also show here how this general algebra can address hidden symmetries present in several quantum systems.
منابع مشابه
Hidden symmetries enhance quantum transport in Light Harvesting systems
For more than 50 years we have known that photosynthetic systems harvest solar energy with almost unit quantum efficiency. However, recent experimental evidence of quantum coherence during the excitonic energy transport in photosynthetic organisms challenges our understanding of this fundamental biological function. Currently, and despite numerous efforts, the causal connection between coherenc...
متن کاملAn Introduction to Yangian Symmetries
Quantum integrable models are characterized by the existence of commuting conserved charges which one is free to choose as Hamiltonians. They usually also possess extra symmetries which are at the origin of degeneracies in the spectrum. These symmetries are often not a group but a quantum group. The Yangians [1] are quantum group symmetries which (almost systematically) show up in integrable mo...
متن کاملTime-Dependent Real-Space Renormalization Group Method
In this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent Hamiltonians. We drive the time-dependent recursion relations for the renormalized tight-binding Hamiltonian by decimating selective sites of lattice iteratively. The formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...
متن کاملIncompleteness of Representation Theory: Hidden symmetries and Quantum Non-Integrability
When regular regions are discovered in the parameter space of a system, where the parameter might be an external field applied to the Hydrogen atom, it usually indicates the existence of new (approximate) integrals of motion, and consequently quantum numbers [1]. In studies of many–body systems, the large number of degrees of freedom generally precludes one from using methods introduced in simp...
متن کاملGauging by symmetries
We propose a new procedure to embed second class systems by introducing Wess-Zumino (WZ) fields in order to unveil hidden symmetries existent in the models. This formalism is based on the direct imposition that the new Hamiltonian must be invariant by gauge-symmetry transformations. An interesting feature in this approach is the possibility to find a representation for the WZ fields in a conven...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008