Time evolution of one photon

  • #1
deepalakshmi
93
6
TL;DR Summary
How to evolve one photon using hamiltonian as beam splitter
During time evolution of one photon with vacuum state with hamiltonian as a^†b+b^†a, the answer is cos(t/ℏ)|0,1⟩+isin(t/ℏ)|1,0⟩. But i don't know how to do calculation to get this answer. Can someone please help me?
I tried to do this calculation:



|0⟩|1⟩(t)=e−iHtℏ|0⟩|1⟩
=(cos(tH/ℏ)−isin(tH/ℏ)) |0⟩|1⟩
=[cos(t/ℏ)−isin(t/ℏ)] H|0⟩|1⟩
=[cos(t/ℏ)−isin(t/ℏ)] [|0⟩|1⟩+i|1⟩|0⟩]

How to proceed?
 
Last edited:

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