# Spin States

• Quarlep
Which normal coordinate system?The spin value 1/2 and two spin states drop out of the Dirac equation. Spin-up and spin-down are chosen more or less arbitrarily, because they are the eigenstates of energy in a static magnetic field along the z-direction (theoretical magnetic fields are always along z...). However, they form a complete basis for spin-1/2 particles, and all spin directions can be written as a linear combination of these two basis states. This means that you can orient the particle in any direction in space, so long as you know the spin value and which basis state(s) the particle is in.f

#### Quarlep

In The Theoritical Minimum we shown all spins states use just two states up and down. How can we do that.?
I am confused about the directions of states and normal coordinate system Can somebody help me ?
Thanks

In The Theoritical Minimum
What does that mean?

If you measure the spin direction of a particle with spin 1/2, the only possible measurements are "up" and "down". If the particle has a different spin, the options are different.
Which normal coordinate system?

The spin value 1/2 and two spin states drop out of the Dirac equation. Spin-up and spin-down are chosen more or less arbitrarily, because they are the eigenstates of energy in a static magnetic field along the z-direction (theoretical magnetic fields are always along z...). However, they form a complete basis for spin-1/2 particles, and all spin directions can be written as a linear combination of these two basis states.

Therefore you can have spin directions in each and any direction. The theory is perfectly well developed and used e.g. in neutron diffraction.