- #1
Ben4000
- 5
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Homework Statement
Express Lx in terms of the commutator of Ly and Lz and, using this result, show that <Lx>=0 for this particle.
The Attempt at a Solution
[Ly,Lz]=i(hbar)Lx
<Lx>=< l,m l Lx l l,m>
then what?
Angular momentum is a measurement of the rotational motion of an object. It is a vector quantity, meaning it has both magnitude and direction, and is defined as the product of an object's moment of inertia and its angular velocity.
In quantum mechanics, angular momentum is a fundamental property of a particle. The expectation value of angular momentum is a way to calculate the average value of a particle's angular momentum in a given state. This value can provide insight into the behavior and properties of the particle.
The Uncertainty Principle states that the more precisely we know the angular momentum of a particle, the less precisely we can know its position. Similarly, the more precisely we know the expectation value of angular momentum, the less precisely we can know its associated measurement.
The units of angular momentum are typically expressed as kg·m²/s. Expectation values do not have physical units, as they are simply a mathematical calculation of the average value of a physical quantity.
Expectation values provide insight into the behavior and properties of particles at the quantum level. They can help predict the outcomes of measurements and provide a deeper understanding of the fundamental laws of nature.