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- https://phys.libretexts.org/Workbench/PH_245_Textbook_V2/15%3A_Waves/15.03%3A_Mathematics_of_WavesA wave is an oscillation that travels through a medium, accompanied by a transfer of energy. Energy transfers from one point to another in the direction of the wave motion. The particles of the medium...A wave is an oscillation that travels through a medium, accompanied by a transfer of energy. Energy transfers from one point to another in the direction of the wave motion. The particles of the medium oscillate up and down, back and forth, or both, around an equilibrium position. Given a function of a wave that is a snapshot of the wave, and is only a function of the position x, the motion of the pulse or wave moving at a constant velocity can be modeled by replacing x with x ∓ vt.
- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_I_-_Classical_Mechanics_(Gea-Banacloche)/12%3A_Waves_in_One_Dimension/12.01%3A_Traveling_WavesIf we think of the momentum of a volume element in the medium as being proportional to the product of the instantaneous density and velocity, we see that for this wave, which is traveling in the posit...If we think of the momentum of a volume element in the medium as being proportional to the product of the instantaneous density and velocity, we see that for this wave, which is traveling in the positive x direction, there is more “positive momentum” than “negative momentum” in the medium at any given time (of course, if the wave had been traveling in the opposite direction, the sign of vmed in Equation (???) would have been negative, and we would have found the opposite re…
- 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/Courses/Merrimack_College/Conservation_Laws_Newton's_Laws_and_Kinematics_version_2.0/24%3A_Waves_in_One_Dimension/24.01%3A_Traveling_WavesIf we think of the momentum of a volume element in the medium as being proportional to the product of the instantaneous density and velocity, we see that for this wave, which is traveling in the posit...If we think of the momentum of a volume element in the medium as being proportional to the product of the instantaneous density and velocity, we see that for this wave, which is traveling in the positive x direction, there is more “positive momentum” than “negative momentum” in the medium at any given time (of course, if the wave had been traveling in the opposite direction, the sign of vmed in Equation (???) would have been negative, and we would have found the opposite re…
- 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/Courses/Muhlenberg_College/MC_%3A_Physics_213_-_Modern_Physics/02%3A_Waves/2.06%3A_Mathematics_of_WavesA wave is an oscillation that travels through a medium, accompanied by a transfer of energy. Energy transfers from one point to another in the direction of the wave motion. The particles of the medium...A wave is an oscillation that travels through a medium, accompanied by a transfer of energy. Energy transfers from one point to another in the direction of the wave motion. The particles of the medium oscillate up and down, back and forth, or both, around an equilibrium position. Given a function of a wave that is a snapshot of the wave, and is only a function of the position x, the motion of the pulse or wave moving at a constant velocity can be modeled by replacing x with x ∓ vt.
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/12%3A_Waves/12.02%3A_Mathematics_of_WavesNote that the angular frequency of the second wave is twice the frequency of the first wave (2ω), and since the velocity of the two waves are the same, the wave number of the second wave is t...Note that the angular frequency of the second wave is twice the frequency of the first wave (2ω), and since the velocity of the two waves are the same, the wave number of the second wave is twice that of the first wave (2k).
- https://phys.libretexts.org/Courses/Prince_Georges_Community_College/General_Physics_I%3A_Classical_Mechanics/63%3A_Quantum_Mechanics/63.02%3A_Quantum_MechanicsYou may wonder: how can it be that a particle is in many places at once, or that the place where it appears is completely unpredictable, or that it is in an unknown state unless we're measuring it, or...You may wonder: how can it be that a particle is in many places at once, or that the place where it appears is completely unpredictable, or that it is in an unknown state unless we're measuring it, or that it can be both a particle and a wave at the same time?
- https://phys.libretexts.org/Bookshelves/University_Physics/University_Physics_(OpenStax)/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/16%3A_Waves/16.03%3A_Mathematics_of_WavesA wave is an oscillation that travels through a medium, accompanied by a transfer of energy. Energy transfers from one point to another in the direction of the wave motion. The particles of the medium...A wave is an oscillation that travels through a medium, accompanied by a transfer of energy. Energy transfers from one point to another in the direction of the wave motion. The particles of the medium oscillate up and down, back and forth, or both, around an equilibrium position. Given a function of a wave that is a snapshot of the wave, and is only a function of the position x, the motion of the pulse or wave moving at a constant velocity can be modeled by replacing x with x ∓ vt.
- https://phys.libretexts.org/Courses/Muhlenberg_College/Physics_122%3A_General_Physics_II_(Collett)/12%3A_Waves/12.03%3A_Mathematics_of_WavesA wave is an oscillation that travels through a medium, accompanied by a transfer of energy. Energy transfers from one point to another in the direction of the wave motion. The particles of the medium...A wave is an oscillation that travels through a medium, accompanied by a transfer of energy. Energy transfers from one point to another in the direction of the wave motion. The particles of the medium oscillate up and down, back and forth, or both, around an equilibrium position. Given a function of a wave that is a snapshot of the wave, and is only a function of the position x, the motion of the pulse or wave moving at a constant velocity can be modeled by replacing x with x ∓ vt.
