# Download Lattice Quantum Mechanics and Difference Operators for Discrete Oscillator Potentials (Berichte Aus Der Physik) fb2

**Andreas L. Ruffing**

- Author:Andreas L. Ruffing
- ISBN:3826566734
- ISBN13:978-3826566738
- Genre:
- Publisher:Shaker Verlag GmbH, Germany (November 15, 1999)
- Pages:50 pages
- Language:
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- ePUB format1355 kb
- DJVU format1822 kb
- Rating:4.1
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The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the.

The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Furthermore, it is one of the few quantum-mechanical systems for which an exact, analytical solution is known.

Starting from the q-Heisenberg algebra, we derive from a few abstract principles a broad class of Schrödinger operators in lattice quantum mechanics for which one can determine explicit eigenvalues and spectral properties

Starting from the q-Heisenberg algebra, we derive from a few abstract principles a broad class of Schrödinger operators in lattice quantum mechanics for which one can determine explicit eigenvalues and spectral properties. This happens by algebras of creators and annihilators. Generalized inhomogeneous q-discrete Hermite polynomials occur via their recurrence relations.

Difference ladder operators for a harmonic Schrödinger oscillator using . The analytic behaviour of classical and difference versions of Hermite polynomials is investigated from two different viewpoints.

Difference ladder operators for a harmonic Schrödinger oscillator using unitary linear lattices. The grid under consideration is a mixed version of an equidistant lattice and a q-linear grid. Several properties of the grid are described. The grids under consideration are referred to by the name unitary linear lattices. The analytic behaviour of classical and difference versions of Hermite polynomials is investigated from two different viewpoints: first using oscillation theory which is important in quantum oscillator systems and second using a factorization method which may serve as a stable numerical investigation of the function systems under investigation.

extended oscillator algebras as generalized deformed oscillator ones is shown to. .

extended oscillator algebras as generalized deformed oscillator ones is shown to provide a. bosonization of several variants of supersymmetric quantum mechanics: parasupersymmet-. The time evolution of operators for q-oscillators is derived for the first time by exploiting the connection between q-deformation algebras and Lie-admissible algebras.

Quantum statistical mechanics plays a major role in many fields such as.

Quantum statistical mechanics plays a major role in many fields such as thermodynamics, plasma physics, solid-state physics, and the study of stellar structure. While the theory of quantum harmonic oscillators is relatively simple, the case of anharmonic oscillators, a mathematical model of a localized quantum particle, is more complex and challenging. This book presents a rigorous approach to the statistical mechanics of such systems, in particular with respect to their actions on a crystal lattice.

Quantum mechanics and classical physics . The particle in a one-dimensional potential energy box is the most mathematically simple example where restraints lead to the quantization of energy levels. Relativity and quantum mechanics . Attempts at a unified field theory . The box is defined as having zero potential energy everywhere inside a certain region, and infinite potential energy everywhere outside that region. For the one-dimensional case in the x direction, the time-independent Schrödinger equation may be written. 1-dimensional potential energy box (or infinite potential well).

Simply put them on a finite difference lattice and observe how some movement here and now causes some . But isn't this simply quantum mechanics ? commutative simultaneously measurable independent from each other not causally related.

Simply put them on a finite difference lattice and observe how some movement here and now causes some movement over there some time later. Analytically, if you look at the dispersion relation p mu p^mu m^2 . omega^2 m^2+k^2, where I have assumed hbar c 1, then you get for the group velocity.

I am reading the book on quantum mechanics by Griffiths. The quanta in the infinite potential well for . There are several forms of discreteness in quantum theory. The simplest one is the discreteness of eigenvalues and the associated countable eigenstates

I am reading the book on quantum mechanics by Griffiths. arise due to the boundary conditions, and the quanta in harmonic oscillator arise due to the commutation relations of the ladder operators, which give energy eigenvalues differing by a multiple of $hbar$. The simplest one is the discreteness of eigenvalues and the associated countable eigenstates. Those arise similarly to the discrete standing waves on a guitar string.

1-D Harmonic Oscillator Hamiltonian (using raising and lowering operators). Physics GRE 4. Statistical Mechanics and Thermodynamics. Commutation relation of raising and lowering operators. 1-D Harmonic Oscillator Energy Eigenvalues. Virial's Theorem for Harmonic Oscillator. 3-D Harmonic Oscillator Energy Eigenvalues. Eigenfunctions and Energy Eigenvalues of a free particle. Physics GRE Equations 6. Special Relativity.

Quantum mechanics can be formulated in three ways, as Heisenberg, Schro¨dinger and Feynman did respectively

Quantum mechanics can be formulated in three ways, as Heisenberg, Schro¨dinger and Feynman did respectively. For the last way, an unknown (. forgotten) forerunner exists, that we have found in a paper by Gregor Wentzel, published before the famous works by Heisenberg and Schro¨dinger, and contemporary with the fundamental works of L. de Broglie. Mechanics and geometrical optics are governed by integral principles which attribute a value to each path in conguration or phase space. The actual motions or propagations are iden-tied by local extrema of this value which we call action. Handbuch der Physik 4