# Understanding Spin & Angular Momentum in Quantum Mechanics

• I
• Silviu
In summary, the conversation discusses the spin-singlet state and the measurement of spin in different directions. It is explained that the singlet state remains unchanged under rotations and the spin components of the two particles will always be opposite, regardless of the basis used to describe the state.

#### Silviu

Hello! I got a bit confused about the fact that the whole the description of spin (and angular momentum) is done in the z direction. So, if we are told that a system of 2 particles is in a singlet state i.e. $$\frac{\uparrow \downarrow -\downarrow \uparrow }{2}$$ does this mean that measuring the spin of the first one on ##\textbf{any}## axis (not only z) will ensure that measuring the spin of the second one will give the opposite result? Or is this form true only for the z axis, and if we want to check on other axis, we need to project the up and down of the z axis onto the orthonormal basis of this other system of axis and work from there? Thank you!

The correctly normalized singlet state is
$$|S=0,M=0 \rangle=\frac{1}{\sqrt{2}} (|1/2,-1/2 \rangle-|1/2,+1/2 \rangle).$$
It's true that if measuring the spin component in an arbitrary direction of particle 1 then the spin component of particle 2 in the same direction is opposite. It doesn't matter which basis you use to describe the spin-singlet state. The reason is that for total spin ##S=0## the state doesn't change under rotations, i.e., you cannot distinguish any spin direction from any other.

## 1. What is spin in quantum mechanics?

Spin is a fundamental property of subatomic particles, such as electrons and protons, that describes their intrinsic angular momentum. It is a quantum mechanical concept that cannot be fully understood in terms of classical physics.

## 2. How does spin relate to angular momentum in quantum mechanics?

Spin is a type of angular momentum that is associated with the rotation of a particle around its own axis. It is one component of the total angular momentum of a particle, which also includes its orbital angular momentum.

## 3. What are the possible values of spin in quantum mechanics?

The possible values of spin in quantum mechanics are quantized, meaning they can only take on discrete values. The most common values are 1/2 and 1, but particles with spin 3/2, 2, and higher have also been observed.

## 4. How is spin measured in quantum mechanics?

Spin is measured using a device called a Stern-Gerlach apparatus, which can detect the direction of a particle's spin. The results of these measurements are quantized, meaning they can only take on specific values corresponding to the possible spin states of the particle.

## 5. What is the significance of spin in quantum mechanics?

Spin plays a crucial role in many aspects of quantum mechanics, including the structure of atoms and the behavior of subatomic particles. It also has important implications for fields such as quantum computing and quantum information theory.