# Quantum Matter Lecture 6

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welcome back where we left off last time we were talking about interacting bosons from a more microscopic standpoint I gonna review a couple of things we did at the end of last lecture and we continue on from there just to remind you where we were we wrote down a Hamiltonian for our interacting bosons we can write in first quantized notation it was sum over particles this is a single particle kinetic energy then there a single particle potential energy as well and then there might be an interaction term I guess the interaction term we were using was you over to sum over i J we used to Delta function interaction or I sorry J but in general you could use more complicated interaction we rewrote rewrote that in second to quantize form as integral dr and then we have side dagger hat operator the kinetic energy operator 2m plus v bar yes this is a function of r also and sie hat of our tamar and then plus you over to an obese i dagger are like this and so these are the Hamiltonians we working with that we chose to Delta function interaction because it

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