# Expectation value of angular momentum

• void19
In summary, the expectation value of angular momentum is a mathematical concept used in quantum mechanics to describe the average value of the angular momentum of a system. It is related to the uncertainty principle and can only give an approximation of the true value. The units of the expectation value depend on the units of the angular momentum operator used in the calculation. It can vary with different quantum states and can be negative in certain cases.
void19
Homework Statement
Express Lx in terms of the commutator of Ly and Lz , show that <Lx>=0 for this particle.
Relevant Equations
[Ly,Lz]=i(hbar)Lx

⟨Lx⟩=⟨l,m|Lx|l,m⟩=−iℏ⟨l,m|[Ly,Lz]|l,m⟩

Last edited:
You need to show some effort.

Eh, well the formula you wrote under the picture gives exactly the required result, you just have to figure it out. Maybe expand a bit more. Also, ##[L_y,L_z] = i\hbar L_x##, so you need to divide by ##\hbar##, not multiply. But that doesn't change the result.

robot6

## 1. What is the expectation value of angular momentum?

The expectation value of angular momentum is a measure of the average value of the angular momentum of a quantum mechanical system. It is calculated by taking the sum of the products of the probabilities of each possible outcome of a measurement and the corresponding angular momentum value.

## 2. How is the expectation value of angular momentum calculated?

The expectation value of angular momentum is calculated using the quantum mechanical operator for angular momentum, L, and the wave function of the system, Ψ. The calculation involves taking the integral of the product of the wave function and the operator, which gives the average value of angular momentum for the system.

## 3. What is the significance of the expectation value of angular momentum?

The expectation value of angular momentum is significant because it provides important information about the quantum state of a system. It can reveal the orientation and magnitude of the angular momentum and can also be used to predict the outcome of a measurement of angular momentum.

## 4. How does the expectation value of angular momentum relate to the uncertainty principle?

The expectation value of angular momentum and the uncertainty principle are closely related. According to the uncertainty principle, the more precisely the angular momentum of a particle is measured, the less certain its position can be known. The expectation value of angular momentum helps to quantify this relationship and shows that these two quantities cannot both be known with perfect certainty.

## 5. Can the expectation value of angular momentum be used to determine the spin of a particle?

Yes, the expectation value of angular momentum can be used to determine the spin of a particle. The spin angular momentum is a type of intrinsic angular momentum and is described by a different quantum mechanical operator than orbital angular momentum. By calculating the expectation value of the spin operator, the average value and orientation of the spin can be determined for a quantum system.

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