Quantum Mechanics Momentum
Quantum Mechanics Momentum - Related Videos
02:43
Quantum Numbers
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2020
It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels. The energy levels are labeled with an n value, where n = 1, 2, 3, etc. Generally speaking, the energy of an electron in an atom is greater for greater values of n. This number, n, is referred to as the principal quantum number. The principal quantum number defines the...
02:45
The Quantum-Mechanical Model of an Atom
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2020
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
09:33
Angular Momentum
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2023
Source: Nicholas Timmons, Asantha Cooray, PhD, Department of Physics & Astronomy, School of Physical Sciences, University of California, Irvine, CA Angular momentum is defined as the product of the moment of inertia and the angular velocity of the object. Like its linear analog, angular momentum is conserved, meaning that the total angular momentum of a system will not change if there are no external torques on the system. A torque is the rotational equivalent of a force. Because it is a...
09:46
Conservation of Momentum
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2023
Source: Nicholas Timmons, Asantha Cooray, PhD, Department of Physics & Astronomy, School of Physical Sciences, University of California, Irvine, CA The goal of this experiment is to test the concept of the conservation of momentum. By setting up a surface with very little friction, collisions between moving objects can be studied, including their initial and final momenta. The conservation of momentum is one of the most important laws in physics. When something is conserved in physics, the...
10:00
Gradient Echo Quantum Memory in Warm Atomic Vapor
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Cited by 2 •
2013
The gradient echo memory is a protocol for storing optical quantum states of light in atomic ensembles. Quantum memory is a key element of a quantum repeater, which can extend the range of quantum key distribution. We outline the operation of the scheme when implemented in a 3-level atomic ensemble.
FAQs
Applying the momentum operator to a position-space wavefunction identifies how momentum is represented within that state. For a momentum eigenstate, the operation returns the same state multiplied by a definite momentum value, and the corresponding spatial form is a plane wave. This distinction separates definite-momentum states from general states, which can contain a distribution of possible measurement values.
A Fourier transform changes the description from position space to momentum space. The resulting momentum-space wavefunction encodes the distribution of momentum values associated with the original state, complementing its spatial wavefunction rather than replacing it. This representation is especially useful when the question concerns how momentum is distributed across a state or how position and momentum descriptions correspond.
The uncertainty principle constrains how sharply position and momentum can be specified together. A state with a narrowly localized position cannot simultaneously have arbitrarily precise momentum, and a state with sharply defined momentum has corresponding implications for spatial localization. This limitation is a property of quantum states, so it must be considered when interpreting momentum distributions and wave-packet behavior.
Classical mechanics can characterize momentum through mass times velocity, but the quantum description assigns momentum to an operator acting on a state. Measurement outcomes therefore depend on the state and may form a distribution rather than a single predetermined value. This framework is needed for analyzing wavefunctions, eigenstates, and systems whose motion is described probabilistically.
Begin with the position-space wavefunction and apply the momentum operator -iℏ∇ when the goal is to examine its momentum-related action. Alternatively, Fourier-transform the wavefunction to obtain its momentum-space representation. The first route emphasizes operator action, while the second exposes the momentum distribution, allowing the chosen representation to match the measurement or analysis.
Momentum analysis provides a common framework for free-particle motion, bound states, scattering, and wave-packet evolution. In each case, the relevant state can be examined through momentum values, momentum distributions, or changes between position and momentum descriptions. These applications connect the formal operator to physical predictions across atomic physics and quantum technologies.
A momentum measurement should be interpreted through the possible values associated with the state, not simply by reading a classical trajectory. Momentum eigenstates produce a definite value, whereas a general wavefunction can yield a distribution of outcomes. The momentum-space representation helps organize that distribution, making it useful for connecting a theoretical state with experimental measurement.