相关论文: Modification of Crum's Theorem for `Discrete' Quan…

The perturbative approach was adopted to develop a temperature-dependent version of non-relativistic quantum mechanics in the limit of low-enough temperatures. A generalized, self-consistent Hamiltonian was therefore constructed for an…

For eleven examples of one-dimensional quantum mechanics with shape-invariant potentials, the Darboux-Crum transformations in terms of multiple pseudo virtual state wavefunctions are shown to be equivalent to Krein-Adler transformations…

Theory of the quantum quartic oscillator is developed with close attention to the energy cutoff one needs to impose on the system in order to approximate the smallest eigenvalues and corresponding eigenstates of its Hamiltonian by…

We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional curved strip. We impose the Dirichlet and Neumann boundary conditions on opposite sides of the strip. The existence of the…

We reformulate the time-independent Schr\"odinger equation as a Maurer-Cartan equation on the superspace of eigensystems of the former equation. We then twist the differential so that its cohomology becomes the space of solutions with a set…

In this article it will be introduced a new theorem, can be considered a generalization of Hellmann-Feynman theorem[1]. The latter used in conjunction with the quantization of the free energy[2] of a quantum system allows to derive…

The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given…

The evolution of a driven quantum system is said to be adiabatic whenever the state of the system stays close to an instantaneous eigenstate of its time-dependent Hamiltonian. The celebrated quantum adiabatic theorem ensures that such pure…

The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…

The quantum evolution equation of Loop Quantum Cosmology (LQC) -- the quantum Hamiltonian constraint -- is a difference equation. We relate the LQC constraint equation in vacuum Bianchi I separable (locally rotationally symmetric) models…

We derive the effective Hamiltonian $H - \mu N$ for open quantum systems with varying particle number from first principles within the framework of non-relativistic quantum statistical mechanics. We prove that under physically motivated…

We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists…

In this paper we revisit the problem of finding hidden symmetries in quantum mechanical systems. Our interest in this problem was renewed by nontrivial degeneracies of a simple spin Hamiltonian used to model spin relaxation in alkali-metal…

Upon revisiting the Hamiltonian structure of classical wavefunctions in Koopman-von Neumann theory, this paper addresses the long-standing problem of formulating a dynamical theory of classical-quantum coupling. The proposed model not only…

In this paper we use the formalism of S.Weinberg in order to construct a mathematical model based on the weak decay of hadrons and nuclei. In particular we consider a model which generalizes the weak decay of the nucleus of the cobalt. We…

We present the formulation of the problem of the coherent dynamics of quantum mechanical two-level systems in the adiabatic region in terms of the differential geometry of plane curves. We show that there is a natural plane curve…

Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely believed not to be solvable by such methods. The novel feature of adaptive perturbation…

We develop a holonomy reduction procedure for general Cartan geometries. We show that, given a reduction of holonomy, the underlying manifold naturally decomposes into a disjoint union of initial submanifolds. Each such submanifold…

We consider an isolated autonomous quantum machine, where an explicit quantum clock is responsible for performing all transformations on an arbitrary quantum system (the engine), via a time-independent Hamiltonian. In a general context, we…

We study effects of perturbation Hamiltonian to quantum spin systems which can include quenched disorder. Model-independent inequalities are derived, using an additional artificial disordered perturbation. These inequalities enable us to…