We propose a generalization of the standard geometric formulation of quantum mechanics, based on the classical Nambu dynamics of free Euler tops. This extended quantum mechanics has in lieu of the standard exponential time evolution, a nonlinear temporal evolution given by Jacobi elliptic functions. In the limit where latter’s moduli parameters are set to zero, the usual geometric formulation o...

We propose a general method that allows to detect the existence of normalizable ground states in supersymmetric quantum mechanical systems with non-Fredholm spectrum. We apply our method to show the existence of bound states at threshold in two important cases: 1) the quantum mechanical system describing H-monopoles; 2) the quantum mechanics of D0 branes. e-mail [email protected] Permanen...

The most peculiar, specifically quantum, features of quantum mechanics — quantum nonlocality, indeterminism, interference of probabilities, quantization, wave function collapse during measurement — are explained on a logical-geometrical basis. It is shown that truths of logical statements about numerical values of quantum observables are quantum observables themselves and are represented in qua...

One of the postulates of quantum mechanics is that the Hamiltonian is Hermitian, as this guarantees that the eigenvalues are real. Recently there has been an interest in asking if H = H is a necessary condition, and has lead to the development of PT -symmetric quantum mechanics. This note shows that any finite physically acceptable non-Hermitian Hamiltonian is equivalent to doing ordinary quant...

In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the presence in the theory of General Uncertainty Relations (GUR). Here Quantum Mechanics with Fundamental Length is obtained as a deformation of Quantum Mechanics. The distinguishing feature of the proposed approach in comparison with previous ones, lies on the fact...

We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical variables. The quantum contribution is given by the term of the second order. To escape technical difficulties related to the infinite dimension of phase space f...

This chapter gives a brief introduction to quantum mechanics. Quantum mechanics can be thought of roughly as the study of physics on very small length scales, although there are also certain macroscopic systems it directly applies to. The descriptor “quantum” arises because in contrast with classical mechanics, certain quantities take on only discrete values. However, some quantities still take...

We discuss the superconformal quantum mechanics arising from the M2-branes. We begin with a comprehensive review on the superconformal quantum mechanics and emphasize that conformal symmetry and supersymmetry in quantum mechanics contain a number of exotic and enlightening properties which do not occur in higher dimensional field theories. We see that superfield and superspace formalism is avai...

Cλ-extended oscillator algebras, where Cλ is the cyclic group of order λ, are introduced and realized as generalized deformed oscillator algebras. For λ = 2, they reduce to the well-known Calogero–Vasiliev algebra. For higher λ values, they are shown to provide in their bosonic Fock space representation some interesting applications to supersymmetric quantum mechanics and some variants thereof:...