The number operator is a quantum mechanical operator that counts the number of particles or excitations in a given quantum state. It plays a crucial role in the framework of quantum mechanics, particularly in systems where particles are indistinguishable, like bosons and fermions, as it helps to describe the occupancy of states in Fock space, aids in the formulation of creation and annihilation operators, and is essential for understanding the second quantization process and quantization of fields.
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