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- https://phys.libretexts.org/Bookshelves/Modern_Physics/Spiral_Modern_Physics_(D'Alessandris)/6%3A_The_Schrodinger_Equation/6.4%3A_Expectation_Values_Observables_and_UncertaintyAn electron is trapped in a one-dimensional infinite potential well of length L. Find the expectation values of the electron’s position and momentum in the ground state of this well. Show that the unc...An electron is trapped in a one-dimensional infinite potential well of length L. Find the expectation values of the electron’s position and momentum in the ground state of this well. Show that the uncertainties in these values do not violate the uncertainty principle.
- https://phys.libretexts.org/Courses/Muhlenberg_College/MC_%3A_Physics_213_-_Modern_Physics/05%3A_The_Schrodinger_Equation/5.04%3A_Expectation_Values_Observables_and_UncertaintyAn electron is trapped in a one-dimensional infinite potential well of length L. Find the expectation values of the electron’s position and momentum in the ground state of this well. Show that the unc...An electron is trapped in a one-dimensional infinite potential well of length L. Find the expectation values of the electron’s position and momentum in the ground state of this well. Show that the uncertainties in these values do not violate the uncertainty principle.
- https://phys.libretexts.org/Courses/Bowdoin_College/Phys1140%3A_Introductory_Physics_II%3A_Part_2/06%3A_Quantum_Mechanics/6.02%3A_Wave_functionsIn quantum mechanics, the state of a physical system is represented by a wave function. In Born’s interpretation, the square of the particle’s wave function represents the probability density of findi...In quantum mechanics, the state of a physical system is represented by a wave function. In Born’s interpretation, the square of the particle’s wave function represents the probability density of finding the particle around a specific location in space. Wave functions must first be normalized before using them to make predictions. The expectation value is the average value of a quantity that requires a wave function and an integration.
- https://phys.libretexts.org/Courses/Muhlenberg_College/MC_%3A_Physics_213_-_Modern_Physics/04%3A_Quantum_Mechanics/4.02%3A_Wave_functionsIn quantum mechanics, the state of a physical system is represented by a wave function. In Born’s interpretation, the square of the particle’s wave function represents the probability density of findi...In quantum mechanics, the state of a physical system is represented by a wave function. In Born’s interpretation, the square of the particle’s wave function represents the probability density of finding the particle around a specific location in space. Wave functions must first be normalized before using them to make predictions. The expectation value is the average value of a quantity that requires a wave function and an integration.
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Introductory_Quantum_Mechanics_(Fitzpatrick)/03%3A_Fundamentals_of_Quantum_Mechanics/3.03%3A_Expectation_Values_(Averages)_and_Varianceswhich is known as the variance of x. (See Chapter [s2].) The square-root of this quantity, σx, is called the standard deviation of x. (See Chapter [s2].) We generally expect the resu...which is known as the variance of x. (See Chapter [s2].) The square-root of this quantity, σx, is called the standard deviation of x. (See Chapter [s2].) We generally expect the results of measurements of x to lie within a few standard deviations of the expectation value.
- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/07%3A_Quantum_Mechanics/7.02%3A_WavefunctionsIn quantum mechanics, the state of a physical system is represented by a wave function. In Born’s interpretation, the square of the particle’s wave function represents the probability density of findi...In quantum mechanics, the state of a physical system is represented by a wave function. In Born’s interpretation, the square of the particle’s wave function represents the probability density of finding the particle around a specific location in space. Wave functions must first be normalized before using them to make predictions. The expectation value is the average value of a quantity that requires a wave function and an integration.
- https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_(Kok)/11%3A_Noncommuting_Operators_and_Uncertainty/11.3%3A_Quantifying_Uncertainty/11.3.2%3A_Uncertainty_in_Quantum_MechanicsIn order to bring this into quantum mechanics, we already know how to calculate the average ⟨a⟩, which we call the “expectation value”. If the state of the system is |ψ⟩ ...In order to bring this into quantum mechanics, we already know how to calculate the average ⟨a⟩, which we call the “expectation value”. If the state of the system is |ψ⟩ and the operator corresponding to the observable a is ˆA, then If the system is in the state |+z⟩, we know that we have a 50% chance each for finding spin-x to be +ℏ/2 or −ℏ/2.
- https://phys.libretexts.org/Bookshelves/Nuclear_and_Particle_Physics/Introduction_to_Applied_Nuclear_Physics_(Cappellaro)/02%3A_Introduction_to_Quantum_Mechanics/2.03%3A_Measurement_and_ProbabilityThe third postulate states also that after the measurement the system is left in the eigenstate corresponding to the eigenvalue found (more generally, if more than one eigenstate is associated to the ...The third postulate states also that after the measurement the system is left in the eigenstate corresponding to the eigenvalue found (more generally, if more than one eigenstate is associated to the same eigenvalue, the state is projected on the subspace of the eigenvalue an, that is, the subspace spanned by all the eigenstates associated with an).
