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Everything about Solid harmonics
Solutions of the Laplace equation in spherical polar coordinates
In physics and mathematics, the solid harmonics are solutions of the Laplace equation in spherical polar coordinates, assumed to be (smooth) functions. There are two kinds: the regular solid harmonics, which are well-defined at the origin and the irregular solid harmonics, which are singular at the origin. Both sets of functions play an important role in potential theory, and are obtained by rescaling spherical harmonics appropriately: Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Solid harmonicsA 5-minute orientation
- Skim a recent paper: Proposal for High-Energy Cutoff Extension of Optical Harmonics of Solid Materials Using the Example of a One-Dimensional ZnO CrystalInfluential work since 2022
- Pick up a classic book: Quantum theory of a particle-oscillator collision applied to gas-surface interactions at cryogenic temperaturesThe most-reprinted book on the subject
- Read the landmark paper: Solid-state harmonics beyond the atomic limitCited 469 times
- Go sideways: Spherical harmonicsA closely related topic
- Go sideways: Laplace's equationA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Solid-state harmonics beyond the atomic limit
Efficient Extreme UV Harmonics Generated from Picosecond Laser Pulse Interactions with Solid Targets
Generation of high-order harmonics from solid surfaces by intense femtosecond laser pulses
Two-Center Integrals over Solid Spherical Harmonics
Bipolar Expansion of Screened Coulomb Potentials, Helmholtz' Solid Harmonics, and their Addition Theorems
Solid harmonics and their addition theorems
Three-center Gaussian-type-orbital integral evaluation using solid spherical harmonics
Properties of the regular and irregular solid harmonics
🆕 Influential since 2022
Proposal for High-Energy Cutoff Extension of Optical Harmonics of Solid Materials Using the Example of a One-Dimensional ZnO Crystal
Defects of the nearest-neighbor tight-binding model in the study of solid harmonics
In-Situ Nanoscale Focusing of Extreme Ultraviolet Solid-State High Harmonics
Investigating acoustoelasticity of plane elastic waves and second harmonics within isotropic solid media: A novel approach
Generation of high-order harmonics with hybrid spin and transverse orbital angular momentum from a crystalline solid
📚 Books worth reading
- 📕Quantum theory of a particle-oscillator collision applied to gas-surface interactions at cryogenic temperaturesJerry D. Smith · 1968
- 📕Recent advances in harmonic analysis and partial differential equationsAndrea R. Nahmod · 2012
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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