Describe the quantum mechanical model
Pro Research Analysisby 
Searched over 200M research papers
Understanding the Quantum Mechanical Model
Introduction to Quantum Mechanical Models
Quantum mechanical models are essential for understanding the behavior of systems at atomic and subatomic scales. These models use mathematical frameworks to describe the properties and interactions of particles, such as electrons and photons, in ways that classical mechanics cannot.
AM1: A Parametric Quantum Mechanical Molecular Model
One significant development in quantum mechanical models is the AM1 (Austin Model 1), which is based on the NDDO (Neglect of Diatomic Differential Overlap) approximation. AM1 addresses the shortcomings of its predecessor, MNDO, particularly in accurately reproducing hydrogen bonds, without increasing computational time. This model has been tested on 167 molecules and currently includes parameters for carbon, hydrogen, oxygen, and nitrogen1.
Quantifying Quantum-Mechanical Processes
Quantum mechanical processes can be quantified using a classical-process model, which helps rule out classical mimicry strategies. This approach has been successfully applied to fundamental quantum mechanics processes, including the dynamics of open quantum systems, quantum-information processing, and energy transfer in photosynthetic complexes. This framework reveals new correlations between entanglement and Einstein-Podolsky-Rosen steering, providing a method for quantifying physical processes2.
Conditionally-Solvable Quantum-Mechanical Models
Some quantum mechanical models are conditionally solvable, meaning they have exact solutions under specific conditions. However, misunderstandings can arise, as seen in models with Coulomb, linear, and harmonic terms. Accurate eigenvalues and eigenfunctions are crucial for deriving correct physical conclusions, which can be achieved using methods like the Ritz variational method3.
Quantum Mechanical Models of Turing Machines
Quantum mechanical models can also be applied to computational systems, such as Turing machines. These models, constructed on a finite lattice of spin-½ systems, operate without energy dissipation and adhere to the time-energy uncertainty principle. This makes them highly efficient, operating at the quantum limit4.
Modeling and Control of Quantum Systems
The modeling and control of quantum systems involve both closed and open quantum systems. Classical control theory, particularly geometric and optimal control, has influenced this field. However, unique tools have been developed to address the probabilistic nature of quantum systems, dissipation effects, and the irreversible nature of measurements. These models are crucial for understanding the controllability and stability of quantum systems5.
Teaching Quantum Mechanics with Mechanical Models
Teaching quantum mechanics can be challenging due to its abstract nature. Mechanical models, such as a particle traveling in a helical path, can help students visualize and understand quantum concepts. These models can be described using both quantum mechanical formalism and derivations from first principles, making them valuable educational tools6.
Quantum Statistical Mechanical Models for Polarizable Fluids
Quantum statistical mechanics can be applied to polarizable fluids using a path-integral approach. This method approximates the quantum mechanical partition function with a classical partition function of a polymer ring. The resulting system can be described by the Ornstein-Zernike equation, providing insights into the dielectric constant, free energy, and internal energy of the model7.
Excitation Energy Transfers in Molecular Systems
A quantum mechanical model has been developed to study excitation energy transfers in molecular systems near interfaces. This model uses time-dependent density functional theory and incorporates solvent effects through the polarizable continuum model. It uniquely includes environment-induced polarizing effects and screening effects in a coherent and self-consistent manner8.
Emergent Quantum Mechanics from Classical Models
Quantum mechanics can emerge from classical mechanics through models that use a local Hamiltonian acting on qubits. These models involve a lattice of classical bits that propagate towards a boundary, where their dynamics are described by Schrödinger's equation. This approach demonstrates how quantum mechanical behavior can arise from classical systems9.
Quantum Mechanical Measurement Process
The quantum mechanical measurement process involves the interaction between an object and a measuring device. Solving the Schrödinger equation for the entire system shows the 'collapse' of the object's wave function. This collapse is a result of the Hamiltonian evolution of the total system, provided the initial measurement device wave function is sharply peaked10.
Conclusion
Quantum mechanical models are diverse and versatile, providing deep insights into the behavior of particles and systems at the quantum level. From molecular modeling to computational systems and educational tools, these models are fundamental to advancing our understanding of the quantum world.
Sources and full results
Most relevant research papers on this topic
Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model
The AM1 quantum mechanical molecular model overcomes MNDO's hydrogen bond limitations without increasing computing time, providing accurate results for 167 molecules.
Highly CitedQuantifying Quantum-Mechanical Processes
Quantum-mechanical processes can be quantified using a generic classical-process model, advancing our understanding of the natural world and paving the way for a generic method for quantifying physical processes.
A most misunderstood conditionally-solvable quantum-mechanical model
This paper reveals that several authors have derived wrong physical conclusions from a gross misunderstanding of the exact eigenvalues and eigenfunctions of a conditionally-solvable quantum-mechanical model.
Quantum Mechanical Models of Turing Machines That Dissipate No Energy
Quantum mechanical models of Turing machines show no energy dissipation and operate near the quantum limit, demonstrating close proximity to the time-energy uncertainty principle.
Highly CitedModeling and Control of Quantum Systems: An Introduction
Quantum systems modeling and control require unique tools to account for their unique features, including probabilistic nature, dissipation, and irreversible measurements.
Highly Cited