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- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/04%3A_Postulates_and_Principles_of_Quantum_MechanicsThis page outlines key principles of quantum mechanics, highlighting that a system's state is defined by a wavefunction that encapsulates all physical information. Observable quantities are linked to ...This page outlines key principles of quantum mechanics, highlighting that a system's state is defined by a wavefunction that encapsulates all physical information. Observable quantities are linked to operators, with measurable outcomes represented by eigenvalues. The time-dependent Schrödinger equation governs wavefunction behavior, while stationary states are derived from the time-independent equation.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/14%3A_Nuclear_Magnetic_Resonance_Spectroscopy/14.03%3A_Proton_NMR_Spectrometers_Operate_at_Frequencies_Between_60_MHz_and_750_MHzThis page discusses the Heisenberg Uncertainty Principle, established by Werner Heisenberg in the mid-1920s. It states that more precise measurement of an electron's position results in greater uncert...This page discusses the Heisenberg Uncertainty Principle, established by Werner Heisenberg in the mid-1920s. It states that more precise measurement of an electron's position results in greater uncertainty in its momentum, due to the wave nature of matter. This principle illustrates fundamental limits in quantum measurements by mathematically expressing the relationship between uncertainties in position and momentum.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Quantum_States_of_Atoms_and_Molecules_(Zielinksi_et_al)/05%3A_Translational_States/5.02%3A_The_Uncertainty_PrincipleThe uncertainty principle is a consequence of the wave property of matter. A wave has some finite extent in space and generally is not localized at a point. Consequently there usually is significant u...The uncertainty principle is a consequence of the wave property of matter. A wave has some finite extent in space and generally is not localized at a point. Consequently there usually is significant uncertainty in the position of a quantum particle in space. Activity 1 at the end of this chapter illustrates that a reduction in the spatial extent of a wavefunction to reduce the uncertainty in the position of a particle increases the uncertainty in the momentum of the particle.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/04%3A_Postulates_and_Principles_of_Quantum_Mechanics/4.E%3A_Postulates_and_Principles_of_Quantum_Mechanics_(Exercises)This page delves into quantum mechanics, covering key concepts such as wavefunctions, operators, and their commutation relations, particularly in the context of angular momentum. It emphasizes the unc...This page delves into quantum mechanics, covering key concepts such as wavefunctions, operators, and their commutation relations, particularly in the context of angular momentum. It emphasizes the uncertainty principle, the role of Hermitian operators, and the time-dependent Schrödinger equation. The text discusses the implications of non-commuting operators, the conditions for eigenvalues, and boundary conditions affecting wavefunctions.
- https://chem.libretexts.org/Bookshelves/General_Chemistry/ChemPRIME_(Moore_et_al.)/05%3A_The_Electronic_Structure_of_Atoms/5.06%3A_The_Uncertainty_PrincipleWhere the electron wave is small (near the ends of the box in all three cases and at the nodes indicated in the figure), there are only a small number of dots. (A node is a place where the intensity o...Where the electron wave is small (near the ends of the box in all three cases and at the nodes indicated in the figure), there are only a small number of dots. (A node is a place where the intensity of the wave is zero, that is, in the guitar-string analogy, where the string has not moved from its rest position.)
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/19%3A_The_First_Law_of_Thermodynamics/19.E%3A_The_First_Law_of_Thermodynamics_(Exercises)This page discusses Werner Heisenberg's 1920s uncertainty principle, which highlights the inverse relationship between the precision of a quantum particle's position and momentum. The principle stems ...This page discusses Werner Heisenberg's 1920s uncertainty principle, which highlights the inverse relationship between the precision of a quantum particle's position and momentum. The principle stems from the wave nature of matter, implying that accurate localization of quantum particles is impossible.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/14%3A_Nuclear_Magnetic_Resonance_Spectroscopy/14.02%3A_Magnetic_Moments_Interact_with_Magnetic_FieldsThis page discusses Werner Heisenberg's uncertainty principle from the 1920s, which states that increasing precision in an electron's position decreases accuracy in its momentum, reflecting a fundamen...This page discusses Werner Heisenberg's uncertainty principle from the 1920s, which states that increasing precision in an electron's position decreases accuracy in its momentum, reflecting a fundamental measurement limit in quantum mechanics. It illustrates these concepts by comparing the uncertainties of position and momentum between a baseball and an electron, emphasizing the distinct quantum behaviors and insights that emerge from such comparisons.
- https://chem.libretexts.org/Courses/University_of_North_Texas/UNT%3A_CHEM_1410_-_General_Chemistry_for_Science_Majors_I/Text/05%3A_The_Electronic_Structure_of_Atoms/5.06%3A_The_Uncertainty_PrincipleWhere the electron wave is small (near the ends of the box in all three cases and at the nodes indicated in the figure), there are only a small number of dots. (A node is a place where the intensity o...Where the electron wave is small (near the ends of the box in all three cases and at the nodes indicated in the figure), there are only a small number of dots. (A node is a place where the intensity of the wave is zero, that is, in the guitar-string analogy, where the string has not moved from its rest position.)
- https://chem.libretexts.org/Bookshelves/General_Chemistry/Concept_Development_Studies_in_Chemistry_(Hutchinson)/05_Quantum_Energy_Levels_in_Atomshe atomic molecular theory provides us a particulate understanding of matter. Each element is characterized as consisting of identical, indestructible atoms with atomic weights which have been determi...he atomic molecular theory provides us a particulate understanding of matter. Each element is characterized as consisting of identical, indestructible atoms with atomic weights which have been determined. Compounds consists of identical molecules, each made up from a specific number of atoms of each of the component elements. We also know that atoms have a nuclear structure, meaning that all of the positive charge and virtually all of the mass of the atom are concentrated in a nucleus.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/09%3A_Chemical_Bonding_in_Diatomic_Molecules/9.11%3A_Photoelectron_Spectra_Support_the_Existence_of_Molecular_OrbitalsThis page discusses Werner Heisenberg's uncertainty principle from the mid-1920s, which illustrates the inverse relationship between the uncertainties of position and momentum for particles. It highli...This page discusses Werner Heisenberg's uncertainty principle from the mid-1920s, which illustrates the inverse relationship between the uncertainties of position and momentum for particles. It highlights that confining a particle's position increases momentum uncertainty, showcasing the wave nature of particles. An exercise compares the uncertainties and wavelengths of a baseball and an electron, offering insights into quantum behaviors versus classical mechanics.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/26%3A_Chemical_Equilibrium/26.13%3A_Homework_ProblemsThis page discusses Werner Heisenberg's uncertainty principle from the mid-1920s, highlighting the inverse relationship between the precision of measuring an electron's position and momentum. It empha...This page discusses Werner Heisenberg's uncertainty principle from the mid-1920s, highlighting the inverse relationship between the precision of measuring an electron's position and momentum. It emphasizes the wave nature of particles that limits exact localization and compares the uncertainties in position between a baseball and an electron to illustrate the differences in quantum and classical behaviors.
