I Can I find a particle in two states simultaneously?

[Ahmed1029]

If I want to get the spin angular momentum of a particle using the Stem-Gerlach experiment, I think I will find the spin 1/2 particle either spin up or spin down, but not both. I however want to ask this : Is there a non-zero probability that a particle which is spin-up in the z direction to be in both states of spin-up and spin-down simultaneously in an arbitrary direction that is not the z direction? Also, could measurement ever find the particle in the two states simultaneously?

 

[PeroK]

If I want to get the spin angular momentum of a particle using the Stem-Gerlach experiment, I think I will find the spin 1/2 particle either spin up or spin down, but not both. I however want to ask this : Is there a non-zero probability that a particle which is spin-up in the z direction to be in both states of spin-up and spin-down simultaneously in an arbitrary direction that is not the z direction? Also, could measurement ever find the particle in the two states simultaneously?

Are you asking about states or measurement outcomes?

Do you understand the concept of superposition of states?

Is there a non-zero probability that a particle which is spin-up in the z direction to be in both states of spin-up and spin-down simultaneously in an arbitrary direction that is not the z direction?

Spin up in the z-direction is a superposition of spin-up and spin down about any other direction.

Also, could measurement ever find the particle in the two states simultaneously?

A measurement does not "find a particle in a state". A measuremement returns a measured value.

 

[martinbn]

If I want to get the spin angular momentum of a particle using the Stem-Gerlach experiment, I think I will find the spin 1/2 particle either spin up or spin down, but not both. I however want to ask this : Is there a non-zero probability that a particle which is spin-up in the z direction to be in both states of spin-up and spin-down simultaneously in an arbitrary direction that is not the z direction? Also, could measurement ever find the particle in the two states simultaneously?

Just to emphasize what PeroK said, a particle is never in two states simultaneously, that makes no sense. It can be in one state that is a superposition of other states.