# Multi-mode Fock states

I would like to ask if this expression makes sense. $$|Ψ⟩ = \frac{1}{\sqrt{7}}(|1000000⟩+|0100000⟩+|0010000⟩+|0001000⟩+|0000100⟩+|0000010⟩+|0000001⟩)$$

For example, $$|1000000⟩$$ represents one particle in the first mode. Can I interpret $$|\Psi\rangle$$ as a wave function of one particle?

• What do the individual states in your superposition mean? For example, what does $|1000000\rangle$ represent? Jan 24 at 21:38
• |1000000⟩ represents one particle in the first mode. Jan 24 at 21:41
• OK. I'm not sure why you only have 7 modes, but assuming the system does indeed only have 7 modes, then what you have written is a state in the 1-particle subspace of the full Fock space. Therefore the state describes on particle, but the mode of the particle is unknown. Jan 24 at 21:45
• Shawn Carol says: " if you have a bunch of different modes and all of them are in are in their n equals one state (all of them are supposed to be one particle) that´s just a complicated wave function for a single particle it acts exactly like that". Did I represent his idea correctly? Thanks Jan 24 at 21:55
• Yes that sounds right and also sounds like what you wrote after you explained what the symbols meant. Jan 24 at 22:08