Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2303.04959 · Boston studies in the philosophy of science

Non-quantum Behaviors of Configuration-Space Density Formulations of Quantum Mechanics

Philipp Roser, Matthew T. Scoggins

Published Nov 21, 2023• 0 citations
arXivHTMLPDF
DOI
10.1007/978-3-031-49861-9_8

Related papers

The configuration space quasi-probability formulation of quantum mechanics

N M Monyonko, L G Wori– Baraja, Manjit Kumar

•Jan 1, 2007•0 citations

Explanation of Relation between Wave Function and Probability Density Based on Quantum Mechanics in Phase Space

Chol Jong, Jin-Sim Kim, Shin-Hyok Jon +1 more

The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.

World Journal of Mechanics•Jan 1, 2023•1 citation

Relational Bundle Geometric Formulation of Non‐Relativistic Quantum Mechanics

Jordan François, Lucrezia Ravera

Abstract A bundle geometric formulation of non‐relativistic many‐particles Quantum Mechanics is presented. A wave function is seen to be a ‐valued cocyclic tensorial 0‐form on configuration space‐time seen as a principal bundle, while the Schrödinger equation flows from its covariant derivative, with the action functional supplying a (flat) cocyclic connection 1‐form on the configuration bundle. In line with the historical motivations of Dirac and Feynman, ours is thus a Lagrangian geometric formulation of QM, in which the Dirac–Feynman path integral arises in a geometrically natural way. Applying the dressing field method , we obtain a relational reformulation of this geometric non‐relativistic QM: a relational wave function is realised as a basic cocyclic 0‐form on the configuration bundle. In this relational QM, any particle position can be used as a dressing field, i.e., as a “physical reference frame.” The dressing field method naturally accounts for the freedom in choosing the dressing field, which is readily understood as a covariance of the relational formulation under changes of physical reference frame.

arXiv:2501.02046•Fortschritte der Physik•Oct 21, 2025•4 citations

QUANTUM MECHANICS WITH DENSITY OPERATORS

Steven M. Moore

Elsevier eBooks•Jan 1, 1978•3 citations

Density Formalism for Quantum Theory

Roderick I. Sutherland

Foundations of Physics•Jul 1, 1998•26 citations

Formulation, interpretation and application of non-commutative quantum mechanics

Frederik G. Scholtz, Laure Gouba, A Hafver +1 more

In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the standard quantum mechanical interpretation based on Positive Operator Valued Measures, provides a sufficient framework for the consistent interpretation of this quantum system. The implications of this formalism for rotational and time reversal symmetry are discussed. The formalism is applied to the free particle and harmonic oscillator in two dimensions and the physical signatures of non commutativity are identified.

arXiv:0812.2803•Journal of Physics A Mathematical and Theoretical•Apr 7, 2009•132 citations
The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.
Abstract A bundle geometric formulation of non‐relativistic many‐particles Quantum Mechanics is presented. A wave function is seen to be a ‐valued cocyclic tensorial 0‐form on configuration space‐time seen as a principal bundle, while the Schrödinger equation flows from its covariant derivative, with the action functional supplying a (flat) cocyclic connection 1‐form on the configuration bundle. In line with the historical motivations of Dirac and Feynman, ours is thus a Lagrangian geometric formulation of QM, in which the Dirac–Feynman path integral arises in a geometrically natural way. Applying the dressing field method , we obtain a relational reformulation of this geometric non‐relativistic QM: a relational wave function is realised as a basic cocyclic 0‐form on the configuration bundle. In this relational QM, any particle position can be used as a dressing field, i.e., as a “physical reference frame.” The dressing field method naturally accounts for the freedom in choosing the dressing field, which is readily understood as a covariance of the relational formulation under changes of physical reference frame.
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the standard quantum mechanical interpretation based on Positive Operator Valued Measures, provides a sufficient framework for the consistent interpretation of this quantum system. The implications of this formalism for rotational and time reversal symmetry are discussed. The formalism is applied to the free particle and harmonic oscillator in two dimensions and the physical signatures of non commutativity are identified.