Quiz on Angular Momentum

What is the formula for angular momentum in classical physics?

• L = m × a

• L = p × v

• L = r × p

• L = r + p

In spherical coordinates, what is the expression for the angular momentum operator?

• L = -iℏ∂/∂θ

• L = -iℏ∂/∂r

• L = -iℏ∂/∂φ

• L = -iℏ∂/∂x

What do the commutation relations of angular momentum help to determine?

• The uncertainty relations

• The speed of light

• The mass of particles

• The charge of particles

What is the eigenvalue equation for L2?

• L2 Υ(θ,ϕ) = k Υ(θ,ϕ)

• L2 Υ(θ,ϕ) = m Υ(θ,ϕ)

• L2 Υ(θ,ϕ) = 0

• L2 Υ(θ,ϕ) = ℏ Υ(θ,ϕ)

What is the value of the magnetic quantum number m?

• m = -1, 0, 1

• m = -l, -l+1, ..., l-1, l

• m = 1, 2, 3

• m = 0, 1, 2

What is the relationship between L2 and Lz?

• L2 and Lz commute

• L2 and Lz do not commute

• L2 is equal to Lz

• L2 is less than Lz

What does the ladder operator L+ do?

• Increases the eigenvalue of Lz by ℏ

• Decreases the eigenvalue of L2

• Decreases the eigenvalue of Lz by ℏ

• Increases the eigenvalue of L2

What is the spin angular momentum for an electron?

• 3/2

• 0

• 1

• 1/2

What is the Pauli spin matrix σz?

• ℏ/2 [0 0; 0 0]

• ℏ/2 [1 1; 1 1]

• ℏ/2 [0 1; 1 0]

• ℏ/2 [1 0; 0 -1]

What is the eigenvalue of L2 in terms of l?

• ℏ²l(l+1)

• ℏ²l

• ℏ²l(l-1)

• ℏ²l²