Ulrich Mutze

This gives a link to the page by page scans of the preprints from all my journal articles.

According to quantum theory, pure physical states correspond to equivalence classes of state vectors, where any two members of one class differ by a complex factor. The point is that such a factor does not change the probability for the occurrence of any measurement result as computed within the formalism of quantum mechanics. In the formalism...

The question is analyzed to what extend a particle which is bound in a space-fixed potential well can be ascribed a time-dependent wave function (pure state) if copies of this system are located near to it — sufficiently close that the particles can exchange energy via a distance-dependent interaction potential. An approximate time step evolution o...

Demographic profiling of a population of sheep buried in toto in the Ptolemaic-Early Roman animal necropolis at Syene/Aswan (Upper Egypt) revealed significantly higher age estimates based on tooth eruption and wear than those based on epiphyseal fusion. Since located in an arid landscape with occasionally heavy dust loads, one plausible assumption...

The aim of this project is to represent an interesting part 1 of computational physics as a system of C++ classes and also to provide a corresponding C++ representation of the mathematical structures and methods that are needed to implement specific physical systems and their behavior. Also 2D and 3D visualization and image processing are treated....

This is an improved version of an earlier work of the same title, but without a version number.

According to quantum theory, pure physical states correspond to equivalence classes of state vectors, where any two members of one class differ by a complex factor. The point is that such a factor does not change the probability for the occurrence of any measurement result as computed within the formalism of quantum mechanics. In the formalism to b...

Visualization is known to help our understanding of physics. This is particularly true for dynamical visualization (animation). The primary dynamical object in quantum mechanics is the wave function. Most of the harder to comprehend quantum behaviors manifest themselves not in a single quantum particle but only in systems of at least two of them. T...

A second order explicit one-step numerical method for the initial value problem of the general ordinary differential equation is proposed. It is obtained by natural modifications of the well-known leapfrog method, which is a second order, two-step, explicit method. According to the latter method, the input data for an integration step are two syste...

For an arbitrary holonomic mechanical system a method for constructing time-discrete trajectories is derived by applying a generalized principle of stationary action to the manifold of those system paths which are parabolic with respect to system of gen-eralized coordinates. The method is applied to the anti-damped harmonic oscillator, and data are...

A computational implementation of quantum dynamics for an arbitrary time-independent Hamilton operator is defined and analyzed. The pro-posed evolution algorithm for a time step needs three additions of state vectors, three multiplications of state vectors with real numbers, and one application of the square of the Hamilton operator to a state vect...

It is shown how the fundamental theorem of calculus for several variables can be used for efficiently computing the electrostatic potential of moderately compli-cated charge distributions. This is exemplified with a charge distribution which resembles the letter F in shape.

A system of 10 elastic polyspherical particles, initially falling freely in the interior of a spherical cavity is simulated employing a time-stepping method and a time-stepping rate which exhibit excellent conservation of to- tal energy. The particles are initially at rest and placed mirror-symmetrically with respect to a vertical plane that divide...

A bijective mapping is established between the set of pure qubit states and the set [0, 1] 3 . This latter set corresponds naturally to the RGB data which most digital image formats associate with the color of pixels. This allows to associate with a digital color image (considered as a [0, 1] 3 -valued matrix) a rectangular lattice of qubits, where...

A second order explicit one-step numerical method for the initial value problem of the general ordinary differential equation is proposed. It is ob-tained by natural modifications of the well-known leap-frog method, which is a second order, two-step explicit method. According to the latter method, the input data for an integration step are two syst...

This paper describes a method to simulate the dynamics of granular sys-tems consisting of irregularly shaped grains. This method is a simplifica-tion and partial improvement of a method that has been developed and employed earlier in simulating the toning process in electro-photographic copiers. Here, grains are modeled as rigidly connected overlap...

A reversible integrator for the time-dependent Sch odinger equation as-sociated with an arbitrary (potentially time-dependent) Hamilton operator is defined. This algorithm assumes the dynamical state of the system to be described by a conventional quantum state vector and a velocity vector of the same data structure and storage size. The algorithm...

This paper describes a method to simulate the dynamics of granular systems consisting of irregularly shaped grains. This method is a simplification and partial improvement of a method that has been developed and employed earlier in simulating the toning process in electro-photographic copiers. Here, grains are modeled as rigidly connected overlappi...

The computational implementation of rotations in three-dimensional space based on quaternions is modified such that three-component objects without constraints play the role of the four-component constraint quater-nions. It is shown that this increases speed and accuracy significantly.

For an arbitrary holonomic mechanical system an integrator is derived by applying an extended principle of stationary action to the manifold of those system paths which are parabolic with respect to the system of generalized coordinates under consideration. A modified variational derivative of the action integral is shown to agree with the force th...

For an arbitrary holonomic mechanical system a method for constructing time-discrete trajectories is derived by applying a generalized principle of stationary action to the manifold of those system paths which are parabolic with respect to system of generalized coordinates. The method is applied to the anti-damped harmonic oscillator, and data are...

The relation between irreducibility and the structure of the commutant is studied for a set of linear bounded operators on a real Hilbert space of arbitrary dimension. The results are applied to the investigation of irreducible sets of semilinear operators on a complex or quaternionic Hilbert space.

Limiting formulas are deduced for the state of a quantum system which is subjected to a rapid sequence of many measurements of the same two-valued observable. In the case of a semibounded Hamiltonian, the dynamics usually gets reduced to the subspace spanned by the eigenstates of the observable. In particular, the values of the observable "freeze."...

The question is analyzed how to describe a closed relativistic system formed by n particlelike constituents. It is proposed that to such a system there corresponds a unitary representation U of the Poincaré group being a function of n(n-1)2 potentials, one for each pair, such that cluster separability holds: If the constituents are grouped into k c...

A manifest Poincare-covariant description of particle position is achieved by extending the Wightman localization of the particle to the whole of spacelike hyperplanes of Minkowski space. Subsequently some related questions are briefly discussed.

A manifestly Poincaré-covariant description of particle position is achieved by extending the Wightman localization of the particle to the whole of spacelike hyperplanes of Minkowski space. Subsequently some related questions are briefly discussed.

The objects under consideration are: A group G containing a subgroup S of finite index p, an irreducible representation (= multiplier representation by unitary or by unitary and antiunitary operators on a Hilbert space of arbitrary dimension) U of G, and an irreducible representation W of S. It is shown (1) that the representations U‖S (the restric...

The objects under consideration are a groupG containing a subgroupN of index 2 and an irreducible multiplier representationU ofG by semiunitary (=unitary or antiunitary) operators on a complex Hilbert space of arbitrary dimension. It is assumed thatU(g) is unitary for allg belonging toN. Then the following assertion is proved. The representation of...

The subject under consideration is a system of n non-interacting particles with spin, being described by a tensor product of n unitary irreducible massive representations of the Poincare group. A unitary transformation that effects a separation of centre-of-mass variables and internal variables is constructed. By means of this transformation, for a...

An axiomatic framework for relativistic direct-interaction single channel scattering theories is formulated in terms of two representations U' and U of the Poincaré group. The infinitesimal generators P (momentum), J (angular momentum), E (energy), N (''boost'') of U, and P', J', E' N' of U' are assumed to be related by the formulas of Bakamjian, T...

For any mass m ≧ 0 and arbitrary spin, free relativistic quantum fields are constructed using the same formulas for m > 0 and for m = 0. The transformation properties of these fields under P, C, T and some questions concerning super-selection rules are discussed.

We give a characterization of the Casimir operators of a Lie algebra by polynomial solutions of a system of first-order partial differential equations. Further an upper bound is stated for the number of independent Casimir operators of a nilpotent Lie algebra.