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- https://chem.libretexts.org/Courses/BethuneCookman_University/B-CU%3ACH-331_Physical_Chemistry_I/CH-331_Text/CH-331_Text/03._The_Schrodinger_Equation_and_a_Particle_In_a_Box/3.09%3A_The_Uncertainty_Principle_ReduxThe operators x and p are not compatible and there is no measurement that can precisely determine both x and p simultaneously. The uncertainty principle is a consequence of the wave property of ma...The operators x and p are not compatible and there is no measurement that can precisely determine both x and p simultaneously. 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.
- https://chem.libretexts.org/Courses/Westminster_College/CHE_180_-_Inorganic_Chemistry/01%3A_Chapter_1_-_Electronic_Structure_of_the_Atom/1.3%3A_Development_of_Quantum_TheoryMacroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. but their exact trajectories cannot be determined. The quantum mechanical m...Macroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. but their exact trajectories cannot be determined. The quantum mechanical model of atoms describes the 3D position of the electron in a probabilistic manner according to a mathematical function called a wavefunction, often denoted as ψ. The squared magnitude of the wavefunction describes the distribution of the probability of finding the electron in a particular region in
- https://chem.libretexts.org/Courses/CSU_San_Bernardino/CHEM_2200%3A_General_Chemistry_II_(Mink)/06%3A_Electronic_Structure_and_Periodic_Properties/6.04%3A_Development_of_Quantum_TheoryMacroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. but their exact trajectories cannot be determined. The quantum mechanical m...Macroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. but their exact trajectories cannot be determined. The quantum mechanical model of atoms describes the 3D position of the electron in a probabilistic manner according to a mathematical function called a wavefunction, often denoted as ψ. The squared magnitude of the wavefunction describes the distribution of the probability of finding the electron in a particular region in
- https://chem.libretexts.org/Courses/GalwayMayo_Institute_of_Technology/Spectroscopy%3A_Background_Information_on_Electronic_Structure_of_Atoms_and_Molecules/01%3A_Chapter_1_-_Electronic_Structure_of_Atoms/1.01%3A_Electronic_Structure_of_Atoms/1.1.04%3A_The_Wave_Behavior_of_MatterAn electron possesses both particle and wave properties. Louis de Broglie showed that the wavelength of a particle is equal to Planck’s constant divided by the mass times the velocity of the particle....An electron possesses both particle and wave properties. Louis de Broglie showed that the wavelength of a particle is equal to Planck’s constant divided by the mass times the velocity of the particle. The electron in Bohr’s circular orbits could thus be described as a standing wave, one that does not move through space. Werner Heisenberg’s uncertainty principle states that it is impossible to precisely describe both the location and the speed of particles that exhibit wavelike behavior.
- https://chem.libretexts.org/Courses/University_of_Georgia/CHEM_3212%3A_Physical_Chemistry_II/03%3A_Quantum_Review/3.1%3A_The_Schr%C3%B6dinger_Equation_and_a_Particle_in_a_Box/3.1.08%3A_The_Uncertainty_Principle_-_Estimating_Uncertainties_from_WavefunctionsThe operators x and p are not compatible and there is no measurement that can precisely determine both x and p simultaneously. The uncertainty principle is a consequence of the wave property of ma...The operators x and p are not compatible and there is no measurement that can precisely determine both x and p simultaneously. 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.
- https://chem.libretexts.org/Courses/Louisville_Collegiate_School/General_Chemistry/LibreTexts_Louisville_Collegiate_School_Chapters_06%3A_Electronic_Structure_and_Periodic_Properties_of_Elements/LibreTexts%2F%2FLouisville_Collegiate_School%2F%2FChapters%2F%2F06%3A_Electronic_Structure_and_Periodic_Properties_of_Elements%2F%2F6.3%3A_Development_of_Quantum_TheoryMacroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. but their exact trajectories cannot be determined. The quantum mechanical m...Macroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. but their exact trajectories cannot be determined. The quantum mechanical model of atoms describes the 3D position of the electron in a probabilistic manner according to a mathematical function called a wavefunction, often denoted as ψ. The squared magnitude of the wavefunction describes the distribution of the probability of finding the electron in a particular region in
- https://chem.libretexts.org/Courses/Widener_University/CHEM_175_-_General_Chemistry_I_(Van_Bramer)/05%3A_Electronic_Structure_and_Periodic_Properties/5.02%3A_Development_of_Quantum_TheoryMacroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. but their exact trajectories cannot be determined. The quantum mechanical m...Macroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. but their exact trajectories cannot be determined. The quantum mechanical model of atoms describes the 3D position of the electron in a probabilistic manner according to a mathematical function called a wavefunction, often denoted as ψ. The squared magnitude of the wavefunction describes the distribution of the probability of finding the electron in a particular region in
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Quantum_Chemistry_with_Applications_in_Spectroscopy_(Fleming)/02%3A_Particle_in_a_Box/2.04%3A_The_Tools_of_Quantum_MechanicsQuantum mechanics is a model that can predict many properties of systems. The prediction of these properties can be made by examining the results of operations on the wavefunctions describing systems....Quantum mechanics is a model that can predict many properties of systems. The prediction of these properties can be made by examining the results of operations on the wavefunctions describing systems. In order to develop a quantum mechanical "toolbox", we utilize the results of the Particle in a Box model.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/01%3A_The_Dawn_of_the_Quantum_TheoryThis page outlines the transformation in physicists' understanding of the mathematical foundations of physics, transitioning from Newtonian mechanics to quantum mechanics. Key developments include the...This page outlines the transformation in physicists' understanding of the mathematical foundations of physics, transitioning from Newtonian mechanics to quantum mechanics. Key developments include the application of the quantum hypothesis to blackbody radiation, Einstein's explanation of the photoelectric effect, and the characterization of the hydrogen atomic spectrum.
- https://chem.libretexts.org/Under_Construction/Purgatory/CHEM_2100%3A_General_Chemistry_I_(Mink)/06%3A_Electronic_Structure_and_Periodic_Properties/6.03%3A_Development_of_Quantum_TheoryMacroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. but their exact trajectories cannot be determined. The quantum mechanical m...Macroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. but their exact trajectories cannot be determined. The quantum mechanical model of atoms describes the 3D position of the electron in a probabilistic manner according to a mathematical function called a wavefunction, often denoted as ψ. The squared magnitude of the wavefunction describes the distribution of the probability of finding the electron in a particular region in
- https://chem.libretexts.org/Courses/CSU_San_Bernardino/CHEM_2100%3A_General_Chemistry_I_(Mink)/06%3A_Electronic_Structure_and_Periodic_Properties/6.04%3A_Development_of_Quantum_TheoryMacroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. but their exact trajectories cannot be determined. The quantum mechanical m...Macroscopic objects act as particles. Microscopic objects (such as electrons) have properties of both a particle and a wave. but their exact trajectories cannot be determined. The quantum mechanical model of atoms describes the 3D position of the electron in a probabilistic manner according to a mathematical function called a wavefunction, often denoted as ψ. The squared magnitude of the wavefunction describes the distribution of the probability of finding the electron in a particular region in
