We study two seminal approaches, developed by B. Simon and J. Kisy\'nski, to the well-posedness of Schr\"odinger equation with a time-dependent Hamiltonian. In both cases Hamiltonian is assumed be semibounded from below have constant form domain but possibly non-constant operator domain. The problem addressed in abstract setting, without assuming any specific functional expression for connectio...

We study the Schrödinger operator −∆ − αδ(x − Γ) in L 2 (R 3) with a δ interaction supported by an infinite non-planar surface Γ which is smooth, admits a global normal parameterization with a uniformly elliptic metric. We show that if Γ is asymptotically planar in a suitable sense and α > 0 is sufficiently large this operator has a non-empty discrete spectrum and derive an asymptotic expansion...

The Schwinger model (quantum electrodynamics with massless fermions in one spatial dimension) is solved, supposing that space is a circle. This clarifies aspects of the usual version of the model, where space is a line, without changing the physics. The Hamiltonian formalism is used. On a circle, an abelian gauge field has one physical degree of freedom, and the gauge covariant Dirac operator, ...

We examine a new application of the Holstein-Primakoff realization of the simple harmonic oscillator Hamiltonian. This involves the use of infinite-dimensional representations of the Lie algebra su(2). The representations contain nonstandard raising and lowering operators, which are nonlinearly related to the standard a† and a. The new operators also give rise to a natural family of two-oscilla...

We study the persistence of Poincaré Treshchev tori on a resonant surface of a nearly integrable Hamiltonian system in which the unperturbed Hamiltonian needs not satisfy the Kolmogorov non-degenerate condition. The persistence of the majority of invariant tori associated to g-nondegenerate relative equilibria on the resonant surface will be shown under a Rüssmann like condition.

A new realization of the fourth-order derivative Pais-Uhlenbeck oscillator is constructed. This realization possesses no states of negative norm and has a real energy spectrum that is bounded below. The key to this construction is the recognition that in this realization the Hamiltonian is not Dirac Hermitian. However, the Hamiltonian is symmetric under combined space reflection P and time reve...

An N2 dimensional representation of the periodic Temperley-Lieb algebra TLL(x) is presented. It is also a representation of the cyclic group ZN . We choose x = 1 and define a Hamiltonian as a sum of the generators of the algebra acting in this representation. This Hamiltonian gives the time evolution operator of a stochastic process. In the finite-size scaling limit, the spectrum of the Hamilto...

The relationship between recommendations of some recent papers on the choice of formula (length, velocity, or acceleration type) for calculating radiative transition probabilities is clarified. The problem of choosing the appropriate formula for use in oscillator strength calculations for many-electron systems has been discussed in a number of recent papers (Starace 1971, 1973, Grant 1974). The...

Given a Poisson structure (or, equivalently, a Hamiltonian operator) P , we show that its Lie derivative Lτ (P ) along a vector field τ defines another Poisson structure, which is automatically compatible with P , if and only if [L τ (P ), P ] = 0, where [·, ·] is the Schouten bracket. This result yields a new local description for the set of all Poisson structures compatible with a given Poiss...