On supersymmetries in nonrelativistic quantum mechanics
نویسنده
چکیده
One-dimensional nonrelativistic systems are studied when time-independent potential interactions are involved. Their supersymmetries are determined and their closed subsets generating kinematical invariance Lie superalgebras are pointed out. The study of even supersymmetries is particularly enlightened through the already known symmetries of the corresponding Schrödinger equation. Three tables collect the even, odd, and total supersymmetries as well as the invariance (super)algebras.
منابع مشابه
کوانتش گرانش و بررسی هندسی مکانیک کوانتمی
We elaborate on some recent results on a solution of the Hilbert-space problem in minisuperspace quantum cosmology and discuss the consequences of making the (geometry of the) Hilbert space of ordinary nonrelativistic quantum systems time-dependent. The latter reveals a remarkable similarity between Quantum Mechanics and General Relativity.
متن کاملDiscrete Symmetries and Supersymmetries – Powerful Tools for Studying Quantum Mechanical Systems
Dicrete symmetries (DS) of the Schrödinger-Pauli equation are applied to reduction of this equation and search for its hidden supersymmetries. General problems of using of DS in quantum mechanics are discussed.
متن کاملMeasurement of time in nonrelativistic quantum and classical mechanics
Possible theoretical frameworks for measurement of (arrival) time in the nonrelativistic quantum mechanics are reviewed. It is argued that the ambiguity between indirect measurements by a suitably introduced time operator and direct measurements by a physical clock particle has a counterpart in the corresponding classical framework of measurement of the Newtonian time based on the Hamiltonian m...
متن کاملTransition Amplitudes within the Stochastic Quantization Scheme
Quantum mechanical transition amplitudes are calculated within the stochastic quantization scheme for the free nonrelativistic particle, the harmonic oscillator and the nonrelativistic particle in a constant magnetic field; we close with free Grassmann quantum mechanics. 1
متن کاملThe Geometry of Supersymmetric Quantum Mechanics
One-dimensional sigma-models with N supersymmetries are considered. For conventional supersymmetries there must be N − 1 complex structures satisfying a Clifford algebra and the constraints on the target space geometry can be formulated in terms of these. In the cases in which the complex structures are simultaneously integrable, a conventional extended superspace formulation is given, with the...
متن کامل