Quantum operations (QO) describe any state change allowed in quantum mechanics, such as the evolution of an open system or the state change due to a measurement. We address the problem of which unitary transformations and which observables can be used to achieve a QO with generally different input and output Hilbert spaces. We classify all unitary extensions of a QO, and give explicit ... [Show full abstract] realizations in terms of free-evolution direct-sum dilations and interacting tensor-product dilations. In terms of Hilbert space dimensionality the free-evolution dilations minimize the physical resources needed to realize the QO, and for this case we provide bounds for the dimension of the ancilla space versus the rank of the QO. The interacting dilations, on the other hand, correspond to the customary ancilla-system interaction realization, and for these we derive a majorization relation which selects the allowed unitary interactions between system and ancilla. Comment: 8 pages, no figures. Accepted for publication on Phys. Rev. A
Chapter

# Grundlagen der Quantenphysik

- June 2016

Authors:

Request Full-text Paper PDF

Request full-text PDF

To read the full-text of this research, you can request a copy directly from the author.

Request full-text

Copy link Link copied

To read the full-text of this research, you can request a copy directly from the author.

## Abstract

In diesem Kapitel werden die Grundlagen und Vorstellungen der Quantenmechanik an Hand einiger einfacher Beispiele deutlich gemacht. Die Schrödinger-Gleichung als Grundgleichung der Quantenmechanik wird diskutiert und durch ihre Anwendung auf konkrete Beispiele verdeutlicht. Diese Beispiele umfassen den eindimensionalen Potentialtopf, den Tunneleffekt durch Potentialbarrieren und den Harmonischen Oszillator. Als Beispiel mehrdimensionaler Problem werden der zwei-dimensionale Potentialtopf und das kugelsymmetrische dreidimensionale Potential und ihre mathematischen Darstellung diskutiert.

ResearchGate Logo

Discover the world's research

- 25+ million members
- 160+ million publication pages
- 2.3+ billion citations

## No full-text available

Request Full-text Paper PDF

To read the full-text of this research,

you can request a copy directly from the author.

Request full-text PDF

## Citations (0)

## References (9)

ResearchGate has not been able to resolve any citations for this publication.

Article

Dieses Lehrbuch will die Studierenden der Physik in die Grundlagen der Atomphysik aus experimenteller und theoretischer Sicht einführen und sie dabei behutsam aber systematisch mit den wichtigsten Methoden des dazu notwendigen quantenmechanischen Rüstzeugs vertraut machen. Die gesonderte Kennzeichnung einzelner Abschnitte nach zwei unterschiedlichen Schwierigkeitsgraden gestattet einerseits dem Anfänger, eine Übersicht über die vielfältigen Erscheinungen und experimentellen Methoden zu gewinnen, andererseits dem mehr Fortgeschrittenen die konsequente quantenmechanische Behandlung grundlegender Probleme nachzuvollziehen. Dadurch ist das Buch ab etwa dem 3. Hochschulsemester Physik geeignet und soll bis zum Hauptexamen ein hilfreicher Begleiter sowohl neben inhaltsgleichen Vorlesungen als auch für Prüfungsvorbereitungen sein. "... Dieses Buch bietet einen guten Zugang zu den grundlegenden Methoden der Quantenmechanik mit denen die Problemstellungen der Atomphysik behandelt werden." W. Resch. Redaktion Nawigator, Universität Wien.

Show abstract

Book

Article

Chapter

We now return to the discussion of scattering in three dimensions. In Chapter 12 we looked only at scattering by repulsive potentials. Now we shall study the effects of an attractive potential.

Show abstract

Article

Article

Reents: Physik per Computer. Spektrum, Weinheim (1996) B. Thaller: Visual Quantum Harmonics

- W Kinzel
- G S Brandt
- H D Dahmen

Gasiorowicz: Quantenphysik, 7

- St

Einführung in die Physik

- P Huber
- H H Staub

## Recommended publications

Book

### Quantenmechanik für Fortgeschrittene (QM II)

January 2005

Die vierte Auflage der Quantenmechanik für Fortgeschrittene wurde grundlegend überarbeitet und behandelt die weiterführenden Themen Vielteilchensysteme, Relativistische Wellengleichungen und Relativistische Felder. Die bereits in der Quantenmechanik des gleichen Autors überzeugende stringente mathematische Darstellung wird durch die Angabe aller Zwischenschritte, durch zahlreiche ... [Show full abstract] Anwendungsbeispiele im Text und Übungen ergänzt. Der Text legt insbesondere durch Darstellung der relativistischen Wellengleichungen und ihrer Symmetrieeigenschaften sowie der quantenfeldtheoretischen Grundlagen das Fundament für das weitere Studium von Festkörperphysik, Kern- und Elementarteilchenphysik und ist im gesamten Hauptstudium ein unentbehrlicher Begleiter.

Article

Full-text available

### Physical realizations of quantum operations

May 2003 · Physical review A, Atomic, molecular, and optical physics

Quantum operations (QO) describe any state change allowed in quantum mechanics, such as the evolution of an open system or the state change due to a measurement. We address the problem of which unitary transformations and which observables can be used to achieve a QO with generally different input and output Hilbert spaces. We classify all unitary extensions of a QO, and give explicit ... [Show full abstract] realizations in terms of free-evolution direct-sum dilations and interacting tensor-product dilations. In terms of Hilbert space dimensionality the free-evolution dilations minimize the physical resources needed to realize the QO, and for this case we provide bounds for the dimension of the ancilla space versus the rank of the QO. The interacting dilations, on the other hand, correspond to the customary ancilla-system interaction realization, and for these we derive a majorization relation which selects the allowed unitary interactions between system and ancilla. Comment: 8 pages, no figures. Accepted for publication on Phys. Rev. A

Article

Full-text available

### Multipartite uncertainty relation with quantum memory

July 2021 · Scientific Reports

We present a new quantum-memory-assisted entropic uncertainty relation for multipartite systems which shows the uncertainty principle of quantum mechanics. Notably, our results recover some well-known entropic uncertainty relations for two arbitrary incompatible observables that demonstrate the uncertainties about the results of two measurements. This uncertainty relation might play a critical ... [Show full abstract] role in the foundations of quantum theory.

Article

Full-text available

### Quantum Nonlocality and Quantum Correlations in the Stern–Gerlach Experiment

April 2018 · Entropy

The Stern-Gerlach experiment (SGE) is one of the foundational experiments in quantum physics. It has been used in both the teaching and the development of quantum mechanics. However, for various reasons, some of its quantum features and implications are not fully addressed or comprehended in the current literature. Hence, the main aim of this paper is to demonstrate that the SGE possesses a ... [Show full abstract] quantum nonlocal character that has not previously been visualized or presented before. Accordingly, to show the nonlocality into the SGE, we calculate the quantum correlations C(z, θ) by redefining the Banaszek-Wódkiewicz correlation in terms of theWigner operator, that is C(z, θ) = 〈Ψ| Ŵ (z, pz)σ (θ)|Ψ〉, where Ŵ (z, pz) is the Wigner operator, σ(θ) is the Pauli spin operator in an arbitrary direction θ and |Ψ〉 is the quantum state given by an entangled state of the external degree of freedom and the eigenstates of the spin. We show that this correlation function for the SGE violates the Clauser-Horne-Shimony-Holt Bell inequality. Thus, this feature of the SGE might be interesting for both the teaching of quantum mechanics and to investigate the phenomenon of quantum nonlocality.

Article

### Fundamentals of quantum information

March 1998 · Physics World

Ever since its invention in the 1920s, quantum physics has given rise to countless discussions about its meaning and about how to interpret the theory correctly. These discussions focus on issues like the Einstein-Podolsky-Rosen paradox, Quantum non-locality and the role of measurement in quantum physics. In recent years, however research into the very foundations of quantum mechanics has also ... [Show full abstract] led to a new field – quantum information technology. The use of quantum physics could revolutionize the way we communicate and process information.

Chapter

Full-text available

### Italian Studies in the Foundations of Quantum Physics. A Bibliography (1965–1985)

January 1988

The following bibliography collects contributions to the foundations of quantum mechanics made by Italian authors from approximately 1965 to 1985, where under this heading we include both new physical, mathematical, and logical results, as well as pieces of philosophical reflection about quantum mechanics.

Book

### Foundations of Quantum Physics

January 2008

Elementary Wave Mechanics.- Quantum Mechanics in One Dimension#x2014 Bound states I.- Time-Dependent States in One Dimension.- Stationary States in One Dimension II.- The Mechanics of Quantum Mechanics.- Harmonic Oscillator Solution Using Operator Methods.- Quantum Mechanics in Three Dimensions#x2014 Angular Momentum.- Central Potentials.- The Hydrogen Atom.- Angular Momentum#x2014 Encore.- ... [Show full abstract] Time-Independent Approximation Methods.- Applications of Time-Independent Approximation Methods.- Atoms in External Fields.- Time-Dependent Perturbations.

Article

Full-text available

### Quantum Thermodynamics

May 2013

Quantum thermodynamics addresses the emergence of thermodynamical laws from
quantum mechanics. The link is based on the intimate connection of quantum
thermodynamics with the theory of open quantum systems. Quantum mechanics
inserts dynamics into thermodynamics giving a sound foundation to
finite-time-thermodynamics. The emergence of the 0-law I-law II-law and III-law
of thermodynamics from ... [Show full abstract] quantum considerations is presented. The emphasis is on
consistence between the two theories which address the same subject from
different foundations. We claim that inconsistency is the result of faulty
analysis pointing to flaws in approximations.

Preprint

Full-text available

### Quantum interference between distant creation processes

April 2023

The search for macroscopic quantum phenomena is a fundamental pursuit in quantum mechanics. It allows us to test the limits quantum physics and provides new avenues for exploring the interplay between quantum mechanics and relativity. In this work, we introduce a novel approach to generate macroscopic quantum systems by demonstrating that the creation process of a quantum system can span a ... [Show full abstract] macroscopic distance. Specifically, we generate photon pairs in a coherent superposition of two origins separated by up to 70 meters. This new approach not only provides an exciting opportunity for foundational experiments in quantum physics, but also has practical applications for high-precision measurements of distributed properties such as pressure and humidity of air or gases.

Book

### Quantenmechanik zu Fuß 1: Grundlagen

January 2024

Article

Full-text available

### Comment on "Foundations of quantum mechanics: Connection with stochastic processes"

November 2000 · Physical review A, Atomic, molecular, and optical physics

Recently, Olavo has proposed several derivations of the Schrodinger equation from different sets of hypothesis ("axiomatizations") [Phys. Rev. A 61, 052109 (2000)]. One of them is based on the infinitesimal inverse Weyl transform of a classically evolved phase space density. We show however that the Schrodinger equation can only be obtained in that manner for linear or quadratic potential ... [Show full abstract] functions. Comment: 3 pages, no figures

Article

Full-text available

### Entropy in Foundations of Quantum Physics

March 2020 · Entropy

Entropy can be used in studies on foundations of quantum physics in many different ways, each of them using different properties of this mathematical object [...]

## Looking for the full-text?

You can request the full-text of this chapter directly from the authors on ResearchGate.

Request full-text

or

Email

Tip: Most researchers use their institutional email address as their ResearchGate login

Keep me logged in

Log in

or

Welcome back! Please log in.

Email
· Hint

Tip: Most researchers use their institutional email address as their ResearchGate login

Keep me logged in

Log in

or

Company

Support

Business solutions

© 2008-2024 ResearchGate GmbH. All rights reserved.