Introduction to Quantum Mechanics

By Eduardo J S Villaseñor. 2008

1,237 citations recorded by the source corpus.

The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual representation of Quantum Mechanics on Hilbert spaces is also discussed.

Subfields: Atomic and Molecular Physics, and Optics

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Tensor Field Networks: Rotation- and Translation-Equivariant Neural Networks for 3D Point Clouds (2018, methodology): “…with u ( l 1 ) ∈ l 1 and v ( l 2 ) ∈ l 2 , u ( l 1 ) ⊗ v ( l 2 ) ∈ l 1 ⊗ l 2 can be calculated using Clebsch-Gordan coefﬁcients (see Grifﬁths [25]) (denoted with C ): This tensor product produces non-zero values only for l between | l 1 − l 2 | and ( l 1 + l 2 ) inclusive ( m is any integer…”
Magnetless Microwave Circulators Based on Spatiotemporally Modulated Rings of Coupled Resonators (2016, background): “The quasi-rotating states exist at different frequency levels , which is a direct evidence that the modulated loop is nonreciprocal.”
Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles (2006, neutral): “Use of orthogonality, (3.9), then gives (3.79).”
Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm (2017, methodology): “[12] Griffiths D (2005) Introduction to Quantum Mechanics.”
Some applications of the Lambert W function to physics (2000, neutral): “ThewavelengthZ dfe^g at which \ is a maximumobeys Wien’s displacement law Z dfe^g [h+ji , where i is Wien’s displacement constant[3].”
Protein docking using spherical polar Fourier correlations (2000, neutral): “These functions are similar to those found in the solution to Schro¨dinger’s equation for the hydrogen atom, 31 but are specially scaled to the dimensions of typical protein domains.”
A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions (2015, neutral): “For the more complete derivation, showing how the nonadiabatic terms appear, see [15].”
Quantum Computation and Quantum Information: Bibliography (2010, neutral): “But inside the well where the potential is zero, the TISE[2] becomes: − ~ 2”
Neural Field Continuum Limits and the Structure–Function Partitioning of Cognitive–Emotional Brain Networks (2023, methodology): “For ƒ(εi) << 1, the Bose-Einstein statistical distribution switches to one described by classical MaxwellBoltzmann statistics [112,113], resulting in the occupation number:”
Perspective on density functional theory. (2012, critical): “Basic quantum textbooks have separate chapters on perturbation theory and semiclassical approximations, but never relate the two [113].”
Quantum Mechanics for Mathematicians (2008, neutral): “An elementary textbook [PW35] provides an introduction to the old quantum theory, including Bohr-Wilson-Sommerfeld quantization rules, and applications of quantum mechanics to chemistry.”
Angular Synchronization by Eigenvectors and Semidefinite Programming (2009, neutral): “np . Such perturbations are derived in standard textbooks on quantum mechanics aiming to find approximations to the energy levels and eigenstates of perturbed time-independent Hamiltonians (see, e.g., [ 20, Chapter 6 ]).”
Integrated Photonics: Fundamentals (2003, neutral): “The waveguide core is formed by further deposition of a high index oxynitride layer, usually via the chemical vapour deposition method (CVD) or the flame hydrolysis deposition (FHD) method [9].”